Greatest Common Factor

Now that you've studied common factors, we are going to take a look at greatest common factors.

Let's take another look at our example of common factors.

Common Factors

common factors

We identified the common factors by circling the factors that were the same for 36 and 48. What if I asked you to identify the Greatest Common Factor?

Yes! That just means, of the common factors, which one is the greatest? For 36 and 48, the Greatest Common Factor is 12. That's the largest number that we circled!


The Greatest Common Factor is often abbreviated in math, and is known as the GCF.

Let's take a look at another example where you will be asked to find the GCF for three different numbers.

Example 2

Greatest common factor

Yes, it does seem like a lot of work, but as you become more comfortable with factors, you may not have to write down all of the factors. You may be able to mentally identify the GCF for the set of numbers that you are working with.

There are times when you are working with larger numbers and even finding the factors is difficult. In this case, you may use a technique called prime factorization (or factor trees) to help you to determine the greatest common factor. Your next lesson will be on using prime factorization to identify the GCF.

More Pre-Algebra Fraction Lessons


We would love to hear what you have to say about this page!

Like Us on Facebook

Recommend this on Google

Algebra Class E-course Members


Sign Up for Algebra Class E-courses

Click here to renew or retrieve a lost password.

Search This Site

Custom Search

Do You Need Help With Your Basic Algebra Skills?

Get access to your FREE Algebraic Expressions E-course. You'll have instant access to video lessons, practice problems, quizzes, and read more....

It's FREE, so try it today!

sign up

Having Trouble with Your Homework?


What People Are Saying...

"I'd like to start off by relaying my sincerest gratitude for your dedication in teaching algebra. Your methodology is by far the simplest to follow, primarily because you take the time to include the small steps in between that most other teachers leave out.

It helps to know why you are doing something. I am 45 and heading to college to get my BS in Business. I need to brush up, hence the visit to your site. Great Job!"

Jimmy - United States

"I stumbled onto your site after I found out that I needed to use some fundamental algebra for an assignment. Turns out I had forgotten some things and your great site helped me remember them like "that" (snap of fingers). The organization of the site let me find exactly what I was looking for so easily. Kudos to you for maintaining such a great resource for students of all ages!"

Tom - United States

"I just wanted to write and basically thank you for making such a wonderful website! I'm 20 years old and about to take a basic placement test for college. I wanted to brush up on my Algebra skills and I stumbled upon your site. I'm amazed at how simple you make it and how fast I'm remembering Algebra! I don't remember getting most of the answers right when I had an actual teacher in front of me teaching this. Thanks a lot!"

Elizabeth - United States

"I am a pensioner living in South Africa. I stumbled on your website, the best thing that could ever happen to me! Your course in Algebra has helped me a lot to better understand the different concepts. Thank you very much for sharing your skills for teaching math to even people like me. Please do not stop, as I am sure that your teachings have helped thousands of people like me all over the world."

Noel - South Africa

This is an amazing program. In one weekend I used it to teach my Grade 9 daughter most of the introductory topics in Linear Relations. I took her up to Rate of Change and now she can do her homework by herself.

Reg - United States

[ ?]

Subscribe To This Site

Add to Google
Add to My Yahoo!
Add to My MSN
Add to Newsgator
Subscribe with Bloglines

Enjoy This Site?
Then why not use the button below, to add us to your favorite bookmarking service?

| Homepage | Contact Me | Privacy Policy | Disclaimer |Affiliates

Return to top
By Karin Hutchinson Copyright© 2009-2013.