Greatest Common Factor Review

Contributor: Elephango Editors. Lesson ID: 10768

How does math factor into your life? When you have to simplify fractions, a simple way is to find the greatest common factor, and we'll show you how, with online games, exercises, and . . . exercises!


Whole Numbers and Operations

learning style
Kinesthetic, Visual
personality style
Grade Level
Middle School (6-8)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

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  • How many multiplication equations can you make to get the answer of 36?
  • Can you find 5 of them?

Come on, let's try!

  • Did you find the 5 multiplication problems with the answer of 36?

Let's go over them and see if you found them all:

  • 1 x 36 = 36
  • 2 x 18 = 36
  • 3 x 12 = 36
  • 4 x 9 = 36
  • 6 x 6= 36

Let's look at one of the multiplication equations for 36:

2 x 18 = 36

In order to understand the Greatest Common Factor, you need to know the parts of a multiplication equation.

In this equation, 2 and 18 are factors. When multiplied together, they make up the product. In this case, the product is 36:

diagram 1

So, when you list all the multiplication equations for the product of 36, you are really finding all the factors for 36!

Look back at the list of multiplication equations for 36. This time, list the factors in order from least to greatest:

diagram 2

Now, let's compare the factors of 36 to the factors of 72.

Just like before, think of all the multiplication equations for 72 and then list out the factors from least to greatest:

diagram 3

First, find all the common factors of 36 and 72. These are factors that appear in both lists - factors that 36 and 72 share:

diagram 4

Next, look at the common factors and find the largest number. This is our Greatest Common Factor!

diagram 5

So, the Greatest Common Factor (GCF) of 36 and 72 is 36!

You could also show this comparison in a Venn diagram. You can see all of the common factors in the middle, but only the largest number is the GCF!

venn diagram

Visit the Got It? section to review finding factors and finding the GCF!

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