problem solving using gcf

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GCF and LCM Explained w/ 7 Step-by-Step Examples!

// Last Updated: November 9, 2020 - Watch Video //

Do you ever get GCF and LCM confused?

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

It happens, right?

Well, today, we’re going to learn the one method that gets you the answers to both very easily.

Let’s go!

But first let’s review the basic definitions of each.

What Is GCF And LCM

The Greatest Common Factor (also known as GCF ) is the largest number that divides evenly into each number in a given set of numbers.

The Least Common Multiple (also known as LCM ) is the smallest positive multiple that is common to two or more numbers.

Why Do You Need Both Methods

So will there ever be a time when we will need to use both the GCF, Greatest Common Factor and LCM, Least Common Multiple?

Yes, whenever we perform operations with fractions !

For instance, we may need to use the LCM to help us add two fractions , and also the GCF to simplify our result .

Consequently, you will need to know how to use both of these techniques at the same time.

How To Find GCF And LCM

How do you keep them straight and not mix them up?

Great question!

First, whenever you are asked to find both the greatest common factor and the least common multiple, always choose the prime factorization method , or the listing of prime factors, as it will save you time and is the only method that will work consistently.

And secondly, use the last letters of GCF and LCM to find what you need!

Here’s a trick: GC F = F ewer and LC M = More

Remember, when using our prime factorization technique , we choose the fewest common factors for the GCF, and for the LCM, we choose the most of each factor as discussed at Minnesota State University .

Example #1 — Two Numbers

Working a few problems will help to make sense of how this works.

For our first question, let’s find the GCF and find the LCM of two numbers: 12 and 18

Find GCF and LCM of Two Numbers — Example

This means that the GCF of (12 and 18) is 6, and the LCM of (12 and 18) is 36.

Example #2 — Three Numbers

Now let’s work a problem involving three numbers.

Find the GCF and LCM of 15, 18, 24

Find GCF and LCM of Three Numbers — Example

• The GCF of (15, 18, and 24) is 3.
• And the LCM of (15, 18, and 24) is 360.

Using prime factorization and our trick for remembering what factors to choose is a snap!

Closing Thoughts

Now, I would like to point out that the phrase GCF has many synonyms. So, if you ever hear or see one of these alternate phrases, don’t be alarmed. Just know they all mean the same thing – find the greatest positive integer that divides evenly into two or more numbers.

The alternative terminologies for the Greatest Common Factor (GCF) are:

• Highest Common Factor (HCF)
• Greatest Common Divisor (GCD)
• Greatest Common Measure (GCM)
• Highest Common Divisor (HCD)

And while there are no alternate terminologies for Least Common Multiple, you will hear Least Common Multiple (LCM) and Least Common Divisor (LCD) used together quite often. Sometimes, they will be used interchangeably .

The LCM is how we find common multiples of two or more numbers, whereas the LCD is the least common multiple in a fraction’s denominator. So, the LCD is a subset or special case of the LCM. But in all honesty, they require the same math process, so many teachers and students use these two phrases as synonyms.

But, regardless of what the technique is called, the process for finding the greatest common factor and the least common multiple is very straightforward.

Worksheet (PDF) — Hands on Practice

Put that pencil to paper in these easy to follow worksheets — expand your knowledge!

GCF and LCM — Practice Problems GCF and LCM — Step-by-Step Solutions

Video Tutorial — Full Lesson w/ Detailed Examples

Together we will work through various exercises involving two and three numbers to master the techniques of finding the GCF and LCM and never getting them mixed up.

• Introduction to Video: GCF and LCM
• 00:00:26 – How do you find the Greatest Common Factor and the Least Common Multiple?
• 00:01:45 – Find both the GCF and LCM (Examples #1-3)
• 00:14:17 – Determine the GCF and the LCM of three numbers (Examples #4-7)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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Greatest Common Factor (GCF) Worksheets

A large collection of GCF worksheets is meticulously drafted for students in grade 5 through grade 8. GCF is also known as 'greatest common divisor'(GCD), 'highest common factor'(HCF), 'greatest common measure'(GCM) or 'highest common divisor'(HCD). Download and print these GCF worksheets to find the GCF of two numbers, three numbers and more. Try some of these handouts for free!

GCF: Descriptive

List the factors for each pair of numbers. Then, compare to determine the GCF of the two numbers. The printable worksheets are categorized into three levels based on the range of numbers.

• Download the set

GCF of Two Numbers: Standard

Use the prime factorization method to find the GCF for each pair of numbers. This batch of multi-level worksheet pdfs contains a total of 150 problems for 5th grade and 6th grade students. Use the answer key to validate your solutions.

GCF of Two Numbers using Venn Diagrams | Easy

Write down the factors for each pair of numbers in the Venn diagram. Then, list out the common factors in the intersection. The largest factor listed in the overlapping region is the GCF. This set includes numbers up to 25.

GCF of Two Numbers using Venn Diagrams | Moderate

Brighten your math class by using Venn Diagrams to find the GCF of two numbers. Featuring numbers up to 99, this compilation requires learners to list out the factors, place the common factors in the overlapping region, and find the GCF.

GCF and Distributive Property

Being good at something isn’t enough, aim for greatness! Choose our pdf worksheets on GCF and Distributive Property and practice rewriting expressions as the product of the GCF and a sum using the property.

Simplify Fractions using GCF | Easy

Find the GCF for the numerator and the denominator of the given fraction in this set of printable worksheets. Then, reduce the fraction to its lowest term by dividing the numerator and denominator by the GCF. Numbers up to 25 are included in this section.

Simplify Fractions using GCF | Moderate

Facilitate better understanding of GCF by reviewing your skill with this bundle of printable worksheets that features numbers up to 99. Practice finding the GCF and simplifying the fraction using the GCF.

GCF, LCM and the Product

There’s a solid relationship between GCF, LCM, and the product of two numbers. Broaden your knowledge with our pdf worksheets and be the first in class to ace this enthralling topic!

GCF of Three Numbers | Easy

In this bunch of 7th grade and 8th grade pdf worksheets, determine the GCF for the set of three numbers. Apply prime factorization method to list out the common factors. Multiply the common factors to obtain the GCF of the three numbers.

GCF of Three Numbers | Moderate

It’s time to get acquainted with GCF of three numbers by working out the exercises in these pdfs covering numbers up to 99. Work out the GCF by finding the product of the prime factors common to all three numbers.

GCF and LCM word problems

Let’s explore GCF and LCM in the real word using heaps of realistic word problems! Solve life-like situations that impel you to think about the applications of great common factor and least common multiple like never before!

GCF of Polynomials

Gain an in-depth knowledge in finding the Greatest Common Factor of polynomials with these high school worksheets available in easy and moderate levels, find the GCF of two or three monomials, GCF of polynomials, find the GCF using the division method and more!

(45 Worksheets)

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7.1 Greatest Common Factor and Factor by Grouping

Learning objectives.

By the end of this section, you will be able to:

• Find the greatest common factor of two or more expressions
• Factor the greatest common factor from a polynomial
• Factor by grouping

Be Prepared 7.1

Before you get started, take this readiness quiz.

Factor 56 into primes. If you missed this problem, review Example 1.7 .

Be Prepared 7.2

Find the least common multiple of 18 and 24. If you missed this problem, review Example 1.10 .

Be Prepared 7.3

Simplify −3 ( 6 a + 11 ) −3 ( 6 a + 11 ) . If you missed this problem, review Example 1.135 .

Find the Greatest Common Factor of Two or More Expressions

Earlier we multiplied factors together to get a product. Now, we will be reversing this process; we will start with a product and then break it down into its factors. Splitting a product into factors is called factoring .

We have learned how to factor numbers to find the least common multiple (LCM) of two or more numbers. Now we will factor expressions and find the greatest common factor of two or more expressions. The method we use is similar to what we used to find the LCM.

Greatest Common Factor

The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.

First we’ll find the GCF of two numbers.

Example 7.1

How to find the greatest common factor of two or more expressions.

Find the GCF of 54 and 36.

Notice that, because the GCF is a factor of both numbers, 54 and 36 can be written as multiples of 18.

Find the GCF of 48 and 80.

Find the GCF of 18 and 40.

We summarize the steps we use to find the GCF below.

Find the Greatest Common Factor (GCF) of two expressions.

• Step 1. Factor each coefficient into primes. Write all variables with exponents in expanded form.
• Step 2. List all factors—matching common factors in a column. In each column, circle the common factors.
• Step 3. Bring down the common factors that all expressions share.
• Step 4. Multiply the factors.

In the first example, the GCF was a constant. In the next two examples, we will get variables in the greatest common factor.

Example 7.2

Find the greatest common factor of 27 x 3 and 18 x 4 27 x 3 and 18 x 4 .

Find the GCF: 12 x 2 , 18 x 3 12 x 2 , 18 x 3 .

Find the GCF: 16 y 2 , 24 y 3 16 y 2 , 24 y 3 .

Example 7.3

Find the GCF of 4 x 2 y , 6 x y 3 4 x 2 y , 6 x y 3 .

Find the GCF: 6 a b 4 , 8 a 2 b 6 a b 4 , 8 a 2 b .

Find the GCF: 9 m 5 n 2 , 12 m 3 n 9 m 5 n 2 , 12 m 3 n .

Example 7.4

Find the GCF of: 21 x 3 , 9 x 2 , 15 x 21 x 3 , 9 x 2 , 15 x .

Find the greatest common factor: 25 m 4 , 35 m 3 , 20 m 2 25 m 4 , 35 m 3 , 20 m 2 .

Find the greatest common factor: 14 x 3 , 70 x 2 , 105 x 14 x 3 , 70 x 2 , 105 x .

Factor the Greatest Common Factor from a Polynomial

Just like in arithmetic, where it is sometimes useful to represent a number in factored form (for example, 12 as 2 · 6 or 3 · 4 ) , 2 · 6 or 3 · 4 ) , in algebra, it can be useful to represent a polynomial in factored form. One way to do this is by finding the GCF of all the terms. Remember, we multiply a polynomial by a monomial as follows:

Now we will start with a product, like 2 x + 14 2 x + 14 , and end with its factors, 2 ( x + 7 ) 2 ( x + 7 ) . To do this we apply the Distributive Property “in reverse.”

We state the Distributive Property here just as you saw it in earlier chapters and “in reverse.”

Distributive Property

If a , b , c a , b , c are real numbers, then

The form on the left is used to multiply. The form on the right is used to factor.

So how do you use the Distributive Property to factor a polynomial? You just find the GCF of all the terms and write the polynomial as a product!

Example 7.5

How to factor the greatest common factor from a polynomial.

Factor: 4 x + 12 4 x + 12 .

Factor: 6 a + 24 6 a + 24 .

Try It 7.10

Factor: 2 b + 14 2 b + 14 .

Factor the greatest common factor from a polynomial.

• Step 1. Find the GCF of all the terms of the polynomial.
• Step 2. Rewrite each term as a product using the GCF.
• Step 3. Use the “reverse” Distributive Property to factor the expression.
• Step 4. Check by multiplying the factors.

Factor as a Noun and a Verb

We use “factor” as both a noun and a verb.

Example 7.6

Factor: 5 a + 5 5 a + 5 .

Try It 7.11

Factor: 14 x + 14 14 x + 14 .

Try It 7.12

Factor: 12 p + 12 12 p + 12 .

The expressions in the next example have several factors in common. Remember to write the GCF as the product of all the common factors.

Example 7.7

Factor: 12 x − 60 12 x − 60 .

Try It 7.13

Factor: 18 u − 36 18 u − 36 .

Try It 7.14

Factor: 30 y − 60 30 y − 60 .

Now we’ll factor the greatest common factor from a trinomial. We start by finding the GCF of all three terms.

Example 7.8

Factor: 4 y 2 + 24 y + 28 4 y 2 + 24 y + 28 .

We start by finding the GCF of all three terms.

Try It 7.15

Factor: 5 x 2 − 25 x + 15 5 x 2 − 25 x + 15 .

Try It 7.16

Factor: 3 y 2 − 12 y + 27 3 y 2 − 12 y + 27 .

Example 7.9

Factor: 5 x 3 − 25 x 2 5 x 3 − 25 x 2 .

Try It 7.17

Factor: 2 x 3 + 12 x 2 2 x 3 + 12 x 2 .

Try It 7.18

Factor: 6 y 3 − 15 y 2 6 y 3 − 15 y 2 .

Example 7.10

Factor: 21 x 3 − 9 x 2 + 15 x 21 x 3 − 9 x 2 + 15 x .

In a previous example we found the GCF of 21 x 3 , 9 x 2 , 15 x 21 x 3 , 9 x 2 , 15 x to be 3 x 3 x .

Try It 7.19

Factor: 20 x 3 − 10 x 2 + 14 x 20 x 3 − 10 x 2 + 14 x .

Try It 7.20

Factor: 24 y 3 − 12 y 2 − 20 y 24 y 3 − 12 y 2 − 20 y .

Example 7.11

Factor: 8 m 3 − 12 m 2 n + 20 m n 2 8 m 3 − 12 m 2 n + 20 m n 2 .

Try It 7.21

Factor: 9 x y 2 + 6 x 2 y 2 + 21 y 3 9 x y 2 + 6 x 2 y 2 + 21 y 3 .

Try It 7.22

Factor: 3 p 3 − 6 p 2 q + 9 p q 3 3 p 3 − 6 p 2 q + 9 p q 3 .

When the leading coefficient is negative, we factor the negative out as part of the GCF.

Example 7.12

Factor: −8 y − 24 −8 y − 24 .

When the leading coefficient is negative, the GCF will be negative.

Try It 7.23

Factor: −16 z − 64 −16 z − 64 .

Try It 7.24

Factor: −9 y − 27 −9 y − 27 .

Example 7.13

Factor: −6 a 2 + 36 a −6 a 2 + 36 a .

The leading coefficient is negative, so the GCF will be negative?

Try It 7.25

Factor: −4 b 2 + 16 b −4 b 2 + 16 b .

Try It 7.26

Factor: −7 a 2 + 21 a −7 a 2 + 21 a .

Example 7.14

Factor: 5 q ( q + 7 ) − 6 ( q + 7 ) 5 q ( q + 7 ) − 6 ( q + 7 ) .

The GCF is the binomial q + 7 q + 7 .

Try It 7.27

Factor: 4 m ( m + 3 ) − 7 ( m + 3 ) 4 m ( m + 3 ) − 7 ( m + 3 ) .

Try It 7.28

Factor: 8 n ( n − 4 ) + 5 ( n − 4 ) 8 n ( n − 4 ) + 5 ( n − 4 ) .

Factor by Grouping

When there is no common factor of all the terms of a polynomial, look for a common factor in just some of the terms. When there are four terms, a good way to start is by separating the polynomial into two parts with two terms in each part. Then look for the GCF in each part. If the polynomial can be factored, you will find a common factor emerges from both parts.

(Not all polynomials can be factored. Just like some numbers are prime, some polynomials are prime.)

Example 7.15

How to factor by grouping.

Factor: x y + 3 y + 2 x + 6 x y + 3 y + 2 x + 6 .

Try It 7.29

Factor: x y + 8 y + 3 x + 24 x y + 8 y + 3 x + 24 .

Try It 7.30

Factor: a b + 7 b + 8 a + 56 a b + 7 b + 8 a + 56 .

Factor by grouping.

• Step 1. Group terms with common factors.
• Step 2. Factor out the common factor in each group.
• Step 3. Factor the common factor from the expression.

Example 7.16

Factor: x 2 + 3 x − 2 x − 6 x 2 + 3 x − 2 x − 6 .

There is no GCF in all four terms. x 2 + 3 x −2 x − 6 Separate into two parts. x 2 + 3 x ⎵ −2 x − 6 ⎵ Factor the GCF from both parts. Be careful with the signs when factoring the GCF from the last two terms. x ( x + 3 ) − 2 ( x + 3 ) ( x + 3 ) ( x − 2 ) Check on your own by multiplying. There is no GCF in all four terms. x 2 + 3 x −2 x − 6 Separate into two parts. x 2 + 3 x ⎵ −2 x − 6 ⎵ Factor the GCF from both parts. Be careful with the signs when factoring the GCF from the last two terms. x ( x + 3 ) − 2 ( x + 3 ) ( x + 3 ) ( x − 2 ) Check on your own by multiplying.

Try It 7.31

Factor: x 2 + 2 x − 5 x − 10 x 2 + 2 x − 5 x − 10 .

Try It 7.32

Factor: y 2 + 4 y − 7 y − 28 y 2 + 4 y − 7 y − 28 .

Access these online resources for additional instruction and practice with greatest common factors (GFCs) and factoring by grouping.

• Greatest Common Factor (GCF)
• Factoring Out the GCF of a Binomial
• Greatest Common Factor (GCF) of Polynomials

Section 7.1 Exercises

Practice makes perfect.

In the following exercises, find the greatest common factor.

3 x , 10 x 2 3 x , 10 x 2

21 b 2 , 14 b 21 b 2 , 14 b

8 w 2 , 24 w 3 8 w 2 , 24 w 3

30 x 2 , 18 x 3 30 x 2 , 18 x 3

10 p 3 q , 12 p q 2 10 p 3 q , 12 p q 2

8 a 2 b 3 , 10 a b 2 8 a 2 b 3 , 10 a b 2

12 m 2 n 3 , 30 m 5 n 3 12 m 2 n 3 , 30 m 5 n 3

28 x 2 y 4 , 42 x 4 y 4 28 x 2 y 4 , 42 x 4 y 4

10 a 3 , 12 a 2 , 14 a 10 a 3 , 12 a 2 , 14 a

20 y 3 , 28 y 2 , 40 y 20 y 3 , 28 y 2 , 40 y

35 x 3 , 10 x 4 , 5 x 5 35 x 3 , 10 x 4 , 5 x 5

27 p 2 , 45 p 3 , 9 p 4 27 p 2 , 45 p 3 , 9 p 4

In the following exercises, factor the greatest common factor from each polynomial.

4 x + 20 4 x + 20

8 y + 16 8 y + 16

6 m + 9 6 m + 9

14 p + 35 14 p + 35

9 q + 9 9 q + 9

7 r + 7 7 r + 7

8 m − 8 8 m − 8

4 n − 4 4 n − 4

9 n − 63 9 n − 63

45 b − 18 45 b − 18

3 x 2 + 6 x − 9 3 x 2 + 6 x − 9

4 y 2 + 8 y − 4 4 y 2 + 8 y − 4

8 p 2 + 4 p + 2 8 p 2 + 4 p + 2

10 q 2 + 14 q + 20 10 q 2 + 14 q + 20

8 y 3 + 16 y 2 8 y 3 + 16 y 2

12 x 3 − 10 x 12 x 3 − 10 x

5 x 3 − 15 x 2 + 20 x 5 x 3 − 15 x 2 + 20 x

8 m 2 − 40 m + 16 8 m 2 − 40 m + 16

12 x y 2 + 18 x 2 y 2 − 30 y 3 12 x y 2 + 18 x 2 y 2 − 30 y 3

21 p q 2 + 35 p 2 q 2 − 28 q 3 21 p q 2 + 35 p 2 q 2 − 28 q 3

−2 x − 4 −2 x − 4

−3 b + 12 −3 b + 12

5 x ( x + 1 ) + 3 ( x + 1 ) 5 x ( x + 1 ) + 3 ( x + 1 )

2 x ( x − 1 ) + 9 ( x − 1 ) 2 x ( x − 1 ) + 9 ( x − 1 )

3 b ( b − 2 ) − 13 ( b − 2 ) 3 b ( b − 2 ) − 13 ( b − 2 )

6 m ( m − 5 ) − 7 ( m − 5 ) 6 m ( m − 5 ) − 7 ( m − 5 )

In the following exercises, factor by grouping.

x y + 2 y + 3 x + 6 x y + 2 y + 3 x + 6

m n + 4 n + 6 m + 24 m n + 4 n + 6 m + 24

u v − 9 u + 2 v − 18 u v − 9 u + 2 v − 18

p q − 10 p + 8 q − 80 p q − 10 p + 8 q − 80

b 2 + 5 b − 4 b − 20 b 2 + 5 b − 4 b − 20

m 2 + 6 m − 12 m − 72 m 2 + 6 m − 12 m − 72

p 2 + 4 p − 9 p − 36 p 2 + 4 p − 9 p − 36

x 2 + 5 x − 3 x − 15 x 2 + 5 x − 3 x − 15

Mixed Practice

In the following exercises, factor.

−20 x − 10 −20 x − 10

5 x 3 − x 2 + x 5 x 3 − x 2 + x

3 x 3 − 7 x 2 + 6 x − 14 3 x 3 − 7 x 2 + 6 x − 14

x 3 + x 2 − x − 1 x 3 + x 2 − x − 1

x 2 + x y + 5 x + 5 y x 2 + x y + 5 x + 5 y

5 x 3 + 3 x 2 − 5 x − 3 5 x 3 + 3 x 2 − 5 x − 3

Everyday Math

Area of a rectangle The area of a rectangle with length 6 less than the width is given by the expression w 2 − 6 w w 2 − 6 w , where w = w = width. Factor the greatest common factor from the polynomial.

Height of a baseball The height of a baseball t seconds after it is hit is given by the expression −16 t 2 + 80 t + 4 −16 t 2 + 80 t + 4 . Factor the greatest common factor from the polynomial.

Writing Exercises

The greatest common factor of 36 and 60 is 12. Explain what this means.

What is the GCF of y 4 , y 5 , and y 10 y 4 , y 5 , and y 10 ? Write a general rule that tells you how to find the GCF of y a , y b , and y c y a , y b , and y c .

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific!

…with some help. This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential—every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no - I don’t get it! This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need.

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Understanding multiplication

Add and subtract within 100

GCF and LCM

Here you will learn about GCF and LCM (greatest common factor and least common multiple), including how to find the GCF and LCM of two or more numbers using the prime factorization method and recognize when to find the GCF or the LCM in word problems.

Students will first learn about GCF and LCM as part of the number system in 6th grade.

What is GCF and LCM?

GCF and LCM are two abbreviations for the greatest common factor (GCF) and the least common multiple (LCM).

• The GCF is the largest whole number that two or more numbers can be divided by. Other names for this include the greatest common divisor (GCD) and the highest common factor (HCF). For example, find the GCF of 8 and 12. Let’s start by writing the factors of 8 and 12. Factors of {\bf{8}} {\textbf{: }} 1, 2, 4, 8 Factors of {\bf{12}} {\textbf{: }} 1, 2, 3, 4, 6, 12 There are several numbers that occur in both lists ( 1, 2, and 4 ). The largest factor that occurs in each list is 4, and so the greatest common factor of 8 and 12 is \bf{4}.
• The LCM is the smallest whole number that is a multiple of two or more whole numbers (exists within the multiplication table of each number). Another name for this is the lowest common multiple. For example, find the LCM of 8 and 12. Let’s start by writing the first 12 multiples of 8 and 12. Multiples of {\bf{8}} {\textbf{: }} 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96 Multiples of {\bf{12}} {\textbf{: }} 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144 There are several values that occur in both lists ( 24, 48, 72, and 96 ). The lowest of these is 24, hence the least common multiple of 8 and 12 is \bf{24}.

Prime factor decomposition

To calculate the GCF or LCM of two or more numbers, you can write out a list of factors or multiples as we have above, however, this approach can be very time consuming and can be complicated when dealing with factors and multiples of large numbers ( 3 digit numbers in particular).

You can therefore use prime factorization to find these values.

The fundamental theorem of arithmetic states that every positive whole number greater than one is either a prime number, or can be written as a product of its prime factors. Every number has a unique set of numbers called prime factors.

By presenting prime factors within a Venn diagram , you can quickly determine both the GCF and LCM of the two or more numbers in the question.

For example,

8=2\times{2}\times{2}

12=2\times{2}\times{3}

The intersection of the two circles contains the greatest common factor , where you multiply the values within the intersection together .

Here, the GCF of 8 and 12 is equal to 2\times{2}=4.

The union of the two circles contains the least common multiple where you multiply the values within both circles together .

Here, the LCM of 8 and 12 is equal to 2\times(2\times{2})\times{3}=24.

As the least common multiple is found by multiplying all of the factors together within the Venn diagram, the least common multiple can be found by multiplying the greatest common factor by the remaining prime factors.

This allows you to solve problems where you are given the GCF and LCM of two numbers and you need to determine the original two numbers.

Common Core State Standards

How does this relate to 6th grade math?

• Grade 6 – The Number System (6.NS.4) Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers (1–100) with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 \, as \, 4 (9 + 2).

[FREE] GCF and LCM Worksheet (Grade 6 to 8)

Use this worksheet to check your grade 6 to 8 students’ understanding of the greatest common factors and lowest common multiples of numbers. 15 questions with answers to identify areas of strength and support!

How to find the greatest common factor

In order to find the greatest common factor of two or more numbers:

State the product of prime factors for each number.

Write all the prime factors for each number into a Venn diagram.

Multiply the prime factors in the intersection to find the GCF.

How to find the least common multiple

In order to find the least common multiple of two or more numbers:

Multiply each prime factor in the Venn diagram to find the LCM.

GCF and LCM examples

Example 1: gcf of two simple composite numbers.

Find the greatest common factor of 30 and 42.

2 Write all the prime factors for each number into a Venn diagram.

3 Multiply the prime factors in the intersection to find the GCF.

GCF =2\times{3}=6.

Example 2: LCM of two simple composite numbers

Calculate the least common multiple of 16 and 18.

16=2\times{2}\times{2}\times{2}

18=2\times{3}\times{3}

LCM =(2\times{2}\times{2})\times{2}\times(3\times{3})=8\times{2}\times{9}=144.

Example 3: GCF word problem

120 \ ml of red paint and 156 \ ml of blue paint are mixed together to create a tin of purple paint. The paint is then distributed equally into sample tubes. Each tube must contain the same amount of paint that must be over 20 \ ml.

What is the maximum number of tubes that can be filled with the minimum amount of paint?

120=2\times{2}\times{2}\times{3}\times{5}

156=2\times{2}\times{3}\times{13}

GCF =2\times{2}\times{3}=12.

The total amount of paint is 120 + 156 = 276 \ ml.

Dividing 276 \ ml into 12 equal shares (the GCF), we have

276\div{12}=23.

As each tube must contain over 20 \ ml of paint, we must have 12 tubes, each containing 23 \ ml of paint.

Example 4: LCM word problem

A plumber is fixing multiple leaking pipes. Pipe A drips water every 12 seconds. Pipe B drips water every 22 seconds. Both pipes drip at the same time. How much time passes before they next drip at the same time? Write your answer using minutes and seconds.

22=2\times{11}

LCM =(2\times{3})\times{2}\times{11}=6\times{2}\times{11}=132

132 seconds pass. Converting this to minutes and seconds is 2 minutes and 12 seconds ( 60 + 60 + 12 = 132 , with 60 seconds = 1 minute).

How to find the original values given the GCF and the LCM

In order to find the original values given the GCF and the LCM:

• Divide the LCM by the GCF.

Calculate the product of primes of the remainder.

Determine which prime factors match each original number.

Example 5: find the numbers, given the GCF

The greatest common factor of 3 numbers is 7. The product of their remaining prime factors is 30 and each number is greater than 10. Determine the value of the three numbers.

Divide the LCM by the GCF to determine the remainder.

As we already know the remainder ( 30 ), we can move on to step 2.

Using a prime factor tree, the product of primes for 30 is:

30=2\times{3}\times{5}

As each value is greater than 10, the GCF 7 must be a factor of all 3 numbers and it must be multiplied by another factor. 30 has 3 prime factors, 2, 3, and 5 and so the original three numbers are:

A=7\times{2}=14

B=7\times{3}=21

C=7\times{5}=35

Example 6: find the original numbers given the GCF and LCM

Two numbers, A and B, have the following number properties:

• GCF (A,B) = 7
• LCM (A,B) = 2,310
• A is divisible by 3
• B is an even number
• 100<A<B

Determine the values of A and B.

2310\div{7}=330

Using a prime factor tree, the product of primes for 330 is:

330=2\times{3}\times{5}\times{11}

As A is divisible by 3, two factors of A must be 3 and 7 (the GCF).

As B is even, two factors of B must be 2 and 7 (the GCF).

Writing this up so far, we have

A=3\times{7}\times{x}

B=2\times{7}\times{y}

As 330=2\times{3}\times{5}\times{11}, we have the remaining factors of 5 and 11 to place.

As 100<A<B, both A and B are greater than 100 with A being smaller than B. The only way this is possible is by making x=5 and y=11.

This means that,

A=3\times{7}\times{5}=105

B=2\times{7}\times{11}=154

The solution is A = 105 and B = 154.

Tips for teaching GCF and LCM

• Before introducing GCF and LCM, students should have a strong understanding of factors and multiples, which they would have first learned in 4th grade. Review these terms and practice listing factors and multiples if needed.

Easy mistakes to make

• Finding the GCF instead of the LCM (and vice versa) A very common misconception is mixing up the greatest common factor with the least common multiple. Factors are composite numbers that are split into smaller factors. Multiples are composite numbers that are multiplied to make larger numbers.
• Incorrect evaluation of powers It is possible to write prime factors into a Venn diagram with their associated exponent or power. This only becomes an issue when the powers are not correctly interpreted. We suggest having students write the prime factors without the use of exponents. Take, for example, the numbers 12 and 18. 12=2^{2}\times{3} 18=2\times{3}^{2} Here, 2^{2}=2\times{2}=4 which is correct, however, the same misconception could then be continued to 3^{2}=3\times{2}=6, which is incorrect. Instead, 3^{2}=3\times{3}=9. This will have an impact on the value of the GCF and the LCM.

Related lessons on factors and multiples

• Factors and multiples
• Factor tree
• Least common multiple
• Greatest common factor
• Prime factors
• Factor pairs

Practice GCF and LCM questions

1. Find the GCF of 54 and 60.

GCF (54,60) = 2\times{3}=6

2. Find the LCM of 24 and 32.

LCM (24,32) = 3\times(2\times{2}\times{2})\times(2\times{2})=3\times{8}\times{4}=96

3. Two lengths of ribbon measure 1.2 \ m and 80 \ cm. Each piece of ribbon needs to be cut into the fewest number of pieces of the same length. What is the length of each piece?

GCF (80,120) = 2\times{2}\times{2}\times{5}=40

4. Two runners leave the start line of a 200 \ m track on the whistle. It takes runner A \ 1 minute to run 1 lap of the track and runner B \ 1 minute and 12 seconds. What distance will runner B have traveled when they next cross the start line at the same time?

Converting both lap times to seconds, runner A takes 60 seconds, and runner B takes 72 seconds.

GCF (60,72)=2\times{2}\times{3}=12

LCM (60,72) = 5 \times 12 \times (2 \times 3)=5 \times 12 \times 6=360

360 seconds = 6 minutes

6\div{1.2}=5 laps

5. The greatest common factor of two numbers is 35. The product of the remaining factors is 33. Both original numbers contain three digits. What is the difference between the two original numbers?

Smaller number: 35\times{3}=105

Larger number: 35\times{11}=385

6. Two numbers x and y have the following number properties:

• \text{LCM }(x,y)=96
• \text{GCF }(x,y)=8
• 2<x<y<40

What is the value of x+y?

GCF and LCM questions

1. A farm needs to divide their two fields into equal-sized enclosures for some horses. Field 1 is 240 \ m^2. Field 2 is 160 \ m^2. Each horse must have at least 42 \ m^2.

(a) What is the minimum possible area for each enclosure?

(b) What is the maximum number of horses that can use these two fields?

240=2^4 \times 3 \times 5 \, or \, 240=2 \times 2 \times 2 \times 2 \times 3 \times 5

160=2^5 \times 5 \, or \, 160=2 \times 2 \times 2 \times 2 \times 2 \times 5

GCF (240,160)=80 \ m^2

2+3=5 \, or \, (240+160) \div 80=5

2. Given that 6480=2^4 \times 3^4 \times 5, simplify the ratio 10800:6480.

GCF (10800,6480)=2^4 \times 3^3 \times 5

Remaining factors are 5 (for 10800 ) and 3 (for 6480 ).

3. The least common multiple of x and y is 2^3 \times 3^2 \times 5^2 where x is a square number such that 36<x<225.

(a) Find the exact value of x.

(b) The greatest common factor of x and y is 4. Determine the value of y. Use the Venn diagram below to help you.

x=2^2 \times 5^2 or

GCF and LCM FAQs

Step 1: State the product of prime factors for each number. Step 2: Write all the prime factors for each number into a Venn diagram. Step 3: Multiply the prime factors in the intersection to find the GCF.

Step 1: State the product of prime factors for each number. Step 2: Write all the prime factors for each number into a Venn diagram. Step 3: Multiply each prime factor in the Venn diagram to find the LCM.

To find the GCF, list all prime factors that are common between the two numbers and multiply them together. To find the LCM, multiply the GCF by all the prime factors of both numbers that have not yet been used.

The least common denominator (LCD) is the least common multiple (LCM) of the denominators of two or more fractions.

The next lessons are

• Converting fractions, decimals, and percentages
• Fractions operations

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Find out how we can help your students achieve success with our math tutoring programs .

[FREE] Common Core Practice Tests (Grades 3 to 6)

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

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GCF, Distributive Property (Grade 6)

In these lessons, Grade 6 students learn to find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

Related Pages Greatest Common Factor Number Properties Common Core for Grade 6 Grade 6 Math

Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

For example, express 36 + 8 as 4 (9 + 2).

Common Core: 6.NS.4

Suggested Learning Targets

• I can find the greatest common factor and least common multiple.
• I can use the distributive property for whole numbers with no common factor.
• I can apply the Distributive Property to rewrite addition problems by factoring out the Greatest Common Factor.

Component Skills from Previous Grades

The following diagram shows how to use the GCF and Distributive Property to find the sum of two numbers. Scroll down the page for more examples and solutions on GCF and distributive property.

Greatest Common Factor (GCF)

How to find GCF

GCF and Distributive Property

6NS4 - Distributive Property

Example: 3(2 + 6)

6NS4 - Multiple of a Sum

How to write a sum of two whole numbers as a multiple of a sum of two whole numbers?

Example: Use the GCF and the distributive property to express a sum as a product. 20 + 35

Example: Use the GCF and the Distributive Property to express the sum as a product 18 + 27

GCF and the Distributive Property

Step 1: Find the GCF of the 2 numbers Step 2: Re-write using the distributive property.

Example: Use the GCF and the Distributive Property to express the sum. 36 + 8 27 + 18 25 + 60

Example: Apply the distributive property to the algebraic expression. 24x + 18y 10x + 15 16x + 32y

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• What is GCF?
• GCF stands for Greatest Common Factor. The greatest common factor of integers a and b is the largest positive number that is divisible by both a and b without a remainder.
• How to find GCF?
• To find the GCF of two numbers list the factors of each number. Then mark the common factors in both lists. The greatest marked factor is the GCF.
• What GCF is used for?
• GCF (greatest common factor) is the largest positive integer that divides evenly into two or more given numbers. It is commonly used to simplify fractions.

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Newsom called it a ‘gimmick.’ Now he’s using the trick to lower California’s massive deficit

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With a windfall of cash five years ago, Gov. Gavin Newsom said he was doing away with a state budget “gimmick” one of his predecessors relied on to shave about $800 million off a deficit during the Great Recession.

The accounting trick, adopted in 2009, delayed state worker payroll from the end of one fiscal year on June 30 to the start of the next on July 1. A decade later Newsom spent nearly $1 billion to end the subterfuge, with one caveat.

“If I use it in six years, in a recession, forgive me,” Newsom said.

At his urging, Newsom and lawmakers have agreed to use the budget gimmick next year even though California isn’t in a recession.

The tactic is one of several maneuvers Democrats are relying on to reduce a historic budget deficit of at least $37.9 billion by pushing their spending problem forward to another year.

Of the $17.3 billion in budget reductions Newsom and Democrats have agreed to so far, only $3.6 billion are actual cuts.

Lawmakers made the first of those cuts Thursday and passed a budget trailer bill that lowers unspent funding allocations in 2022-23 and 2023-24 by $1.6 billion. Though Newsom touted the changes as part of an “early action” deal to shrink the deficit in Apri l, many of the reductions won’t be reflected in legislation until June or later.

At least so far, Newsom and lawmakers are largely relying on mechanisms other than cuts to shrink the deficit: borrowing $5.2 billion, delaying and deferring $5.2 billion in funding for state-sponsored programs to subsequent years and tapping into $3.4 billion from separate state funds. Democrats also agreed to draw down at least another $12.2 billion from the rainy day fund to cover their spending.

Budget watchers and Republican lawmakers criticized the strategy, saying that resorting to clever accounting now and dipping into California’s savings account while the economy remains strong will make the state more vulnerable to drastic cuts if a recession hits in the years ahead and revenue declines.

Newsom’s critics blame the governor and Democrats for overspending and causing the deficit. The “gimmick” is an example of what his critics view as Democrats failing to make the kind of tough choices that California households are forced to weigh when they spend more money than they bring in.

“They are doing things that you normally do in a recession and there is no recession here,” said David Crane, president of Govern for California, a nonprofit that seeks to oppose the influence of labor unions on state government. “You shouldn’t have to be dipping into reserves to meet a budget deficit if your revenues are 50% higher than they were when you came into office.”

Newsom and Democratic lawmakers detail first California budget cuts totaling $17 billion

Democratic lawmakers and Gov. Gavin Newsom are scrambling to lessen California’s budget deficit, which Newsom estimated at $37.9 billion in January.

April 4, 2024

General fund revenues, which the state uses to pay for most public services, were $140 billion when Newsom took office in in 2018-19. The governor’s January budget assumes revenues of more than $214 billion, an increase of 53%, for the upcoming fiscal year when Democrats plan to cut the rainy day fund in half.

According to the UCLA Anderson Forecast in March , California’s economy is growing faster than the rest of the nation and the possibility of a U.S. recession is fading. Newsom regularly trumpets the strength of the state economy.

“While there are still challenges ahead — notably, state and local government finance, homelessness and out-migration — the forces driving California’s economy remain robust,” UCLA economists wrote.

H.D. Palmer, a spokesperson for the governor’s Department of Finance, said the cuts Democrats have agreed to so far are part, but not all of the solution to the budget woes with more decisions coming in June. He also pointed to the fact that more than 70% of the general fund is spent on K-12 education, healthcare and human services.

“If you don’t agree with these solutions, that’s fine. What specific proposals would you offer up to offset that in terms of programmatic reductions?” he asked of budget critics.

Assembly Republican leader James Gallagher of Yuba City said he would start by funding the fundamentals, such as education, infrastructure and public safety, and then deciding what else the state has resources for.

Newsom often promotes all the one-time funding in his prior budgets, which he said would be easy to stop if the state swung from surplus to shortfall. But he has continued to support many of his expensive political priorities, such as the expansion of Medi-Cal to all eligible low-income immigrants, regardless of their legal status. A state audit also found that California has failed to monitor the effectiveness of its costly homelessness programs , which Newsom and lawmakers have spent $20 billion on over the last five years.

California spent billions on homelessness without tracking if it worked

The California State Auditor’s Office analyzed homelessness spending at the behest of lawmakers concerned about efficacy.

April 9, 2024

“A $73-billion deficit is no joke,” Gallagher said. “It’s a serious problem we’ve got to address. It makes me think that the governor just wants to ride this out until the end of his term and just leave this problem to somebody else.”

A combination of delayed tax deadlines and overspending based on inaccurate budget projections created the budget shortfall, which happens when spending exceeds projected revenues.

Newsom and lawmakers expected revenues to fall below projections because of a declining stock market, high interest rates and increased inflation, but the deficit is much worse than the state accounted for last June. The Newsom administration last pegged the deficit at $37.9 billion in January, though a more recent estimate from the Legislative Analyst’s Office suggests it could be up to $73 billion by the time the governor unveils his revised budget proposal in mid-May.

The state budget in California is largely dependent on income taxes paid by its highest earners. Revenues are prone to volatility, hinging on capital gains from investments, bonuses to executives and windfalls from new stock offerings, and notoriously difficult for the state to predict.

The governor repeatedly blames the shortfall problem on a decision by the federal government to delay the deadline to file 2022 income tax returns from April to November of last year due to winter storms.

In a typical budget year, state government has tax receipts in hand before the governor unveils a revised budget proposal in mid-May and before he reaches a final spending agreement with lawmakers in June. The tax delay forced lawmakers and the governor to enact the current budget in July based on estimates of how much money the state would collect in tax revenues by the November deadline. Those estimates were wildly off.

The legislation approved Thursday goes back and reduces unspent funding in the prior and current budget years. The changes include cutting $45 million for protecting communities from wildfire, $88 million for watershed resilience and reduces funding to expand broadband internet access by $34 million, among other trims.

The bill was part of the “early action” lawmakers and the governor announced that they would take in April to lower the deficit by $17.3 billion before the May revise. But only $3.3 billion of the reductions he claimed they would make can be adopted in law now, and the majority will be included in the final budget agreement, along with other reductions, approved this summer.

Newsom and Democrats announce a plan to reduce the enormous budget deficit. How? TBD

Facing a shortfall of at least $38 billion, Gov. Gavin Newsom and legislative leaders said they have agreed to $12 billion to $18 billion in cuts but offered no details.

March 21, 2024

“We put forward this early action plan to protect our progress and safeguard core programs so that we could spend time and energy on the more challenging decisions to close the remaining budget gap responsibly,” said Senate President Pro Tem Mike McGuire (D-Healdsburg) during floor debates in the Senate on Thursday. “And we’re gonna do just that.”

Democrats are attempting to offset the budget crisis before May, when an updated estimate might show an even deeper shortfall. Democrats also took an unusual step of requiring the state finance department to subtract the $17.3 billion from the estimated deficit before the budget is revised in May, making the shortfall appear smaller before many of the changes are reflected in law.

“This budget is nothing but smoke and mirrors, backroom deals done by the party in control,” said Sen. Brian Dahle (R-Bieber).

Delaying payroll from June 30, 2025 to July 1, 2025 is among the changes that Democrats agreed to, but will not vote on until this summer. The move is expected to push $1.6 billion in payroll costs to the 2025-2026 budget year.

While Crane, a political donor of Assembly Speaker Robert Rivas and dozens of other lawmakers, opposes Newsom’s decision to use the budget gimmick again, he said the “biggest sin” is the decision to dip into the state’s reserves in the absence of a recession. Newsom will have to declare a budget emergency in order to do so under state law.

“My one hope is that by the time the May revise comes around, he’s able to say I’m no longer going to have to dive into reserves,” Crane said.

More to Read

Column: Sore losers are trying to recall Newsom, again. They’re robbing voters of their voice

March 1, 2024

Voters say California’s budget deficit is an ‘extremely serious’ problem, poll finds

Jan. 18, 2024

Newsom cuts $2.9 billion from California climate programs, delays an additional $1.9 billion

Jan. 11, 2024

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Taryn Luna covers Gov. Gavin Newsom and California politics in Sacramento for the Los Angeles Times.

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Course: Algebra 2   >   Unit 3

• Taking common factor from binomial
• Taking common factor from trinomial
• Taking common factor: area model

Factoring polynomials by taking a common factor

• Factor polynomials: common factor

What you should be familiar with before this lesson

What you will learn in this lesson, the distributive property: a ( b + c ) = a b + a c ‍  , check your understanding.

• (Choice A)   ( 2 x ) ( 3 x ) ( 5 ) ‍   A ( 2 x ) ( 3 x ) ( 5 ) ‍  
• (Choice B)   2 x ( 3 x + 5 ) ‍   B 2 x ( 3 x + 5 ) ‍  
• (Choice C)   6 x 2 + 10 x ‍   C 6 x 2 + 10 x ‍  

Factoring out the greatest common factor (GCF)

• Find the GCF of all the terms in the polynomial.
• Express each term as a product of the GCF and another factor.
• Use the distributive property to factor out the GCF.
• 2 x 3 = 2 ⋅ x ⋅ x ⋅ x ‍  
• 6 x 2 = 2 ⋅ 3 ⋅ x ⋅ x ‍  
• 2 x 3 = ( 2 x 2 ) ( x ) ‍  
• 6 x 2 = ( 2 x 2 ) ( 3 ) ‍  
• The first will be 2 x 3 2 x 2 = x ‍   .
• The second term will be 6 x 2 2 x 2 = 3 ‍   .
• (Choice A)   6 x ( 2 x + 18 x ) ‍   A 6 x ( 2 x + 18 x ) ‍  
• (Choice B)   6 x ( 2 x + 3 ) ‍   B 6 x ( 2 x + 3 ) ‍  
• (Choice C)   6 x ( 3 + 12 x 2 ) ‍   C 6 x ( 3 + 12 x 2 ) ‍  

Can we be more efficient?

Factoring out binomial factors, different kinds of factorizations.

• We factored monomials by writing them as a product of other monomials. For example, 12 x 2 = ( 4 x ) ( 3 x ) ‍   .
• We factored the GCF from polynomials using the distributive property. For example, 2 x 2 + 12 x = 2 x ( x + 6 ) ‍   .
• We factored out common binomial factors which resulted in an expression equal to the product of two binomials. For example:

Challenge problems

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Solving women’s health issues through engineering focus of course

Women’s health through the lifespan has been getting a new focus in recent years from the local to the federal level, with President Joe Biden recently launching initiatives to boost federally funded research in this long-overlooked area. That focus is also active in the McKelvey School of Engineering at Washington University in St. Louis, where a new Department of Biomedical Engineering elective course is filled with students interested in how they can use engineering to solve problems in women’s health. 

The “Engineering for Women’s Health” course (BME 4780/5780), available to undergraduate and graduate students, is taught by Michelle Oyen, an associate professor of biomedical engineering and director of the Center for Women’s Health Engineering. Initially, Oyen offered 16 seats in the course, but demand quickly led her to increase the number of students to 48. 

The course includes lectures on women’s reproductive anatomy and physiology, guest speakers from FemTech (technology focused on women’s health) companies and startups, research scientists from the School of Medicine, case studies and panel discussions. 

“When we pull in the engineers from these startup companies, students can talk to the people who work in real jobs in the field,” Oyen said. “The FemTech sector has a lot of startups in women’s health, which is a trillion-dollar market. There are a lot of opportunities for young engineers to work in this space.” 

One class meeting recently featured Christine O’Brien, an assistant professor of biomedical engineering and co-founder and chief scientific officer of Armor Medical Inc., and Kelsey Mayo, co-founder and CEO of Armor Medical. O’Brien and Mayo presented students with their investor pitch and details about how the company got started. They also shared information about their device, a wrist-worn early monitoring system for obstetric hemorrhage, severe blood loss that occurs in 5% of all births and is 90% preventable if detected and treated early. 

Mayo, who survived hemorrhage, told students the company is her “passion project” and encouraged them to find their own. 

“Your day job should be where your passion meets the world’s needs,” she said. “That’s a cool thing for biomedical engineers to consider.” 

Oyen said focusing on the FemTech sector is important for students’ education and gives them an idea of what they can do after they graduate. 

“Part of what has happened over the past decade is shining a light on the fact that there are all these issues that were once only whispered about by women and not brought out into the open,” Oyen said. “People have now realized this is really important because there are unmet needs in health care, which has huge implications. The two most common surgeries for women are a C-section and a hysterectomy. Half of women have a hysterectomy by age 65, which is huge.” 

In the course, students are completing group projects to address needs in women’s health, including menopause, osteoporosis, hip fractures and lack of muscle mass. 

Annika Avula, a dual-degree student earning a bachelor’s and a master’s in biomedical engineering, said she wanted to take this course after taking O’Brien’s course “Quantitative Physiology II” (BME 301B) last fall.

“It really opened so many people’s eyes to things that can be done for women’s health,” Avula said. “This course has introduced me to a new way of thinking. I’m more interested in problems and more called to ask questions.” 

Ella Hanson, a senior earning a bachelor’s and a master’s in biomedical engineering, said she took the course because of her interest in women’s health problems. 

“Dr. Oyen and Dr. O’Brien are addressing the huge gap in BME in the women’s health field,” Hanson said. “We are learning that there are more opportunities out there in engineering beyond orthopedics and other biomedical problems.”

Avula’s group project is looking at the effects of menopause, and Hanson’s group project is looking at endometriosis, a chronic disease that affects 11% of women of reproductive age in the U.S. and for which there is no cure. 

Oyen said that while it took her some time to get comfortable using words about women’s health in front of audiences, her students are open to talking about women’s health issues and using the vocabulary, which she finds encouraging for future generations. 

“I realized that I’m not going to be the one to change the world, but I’m going to teach the ones who will,” Oyen said. 

Originally published on the McKelvey School of Engineering website

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