Arithmetic Grade Six

Lesson Ninety-four: Greatest Common Factors


For any two numbers there exists a single greatest common factor (gcf). For instance, the greatest common factor of 16 and 24 is 8. Here's how you find it:

Step One: List the factors for both numbers:

16: 1, 2, 4, 8, 16.
24: 1, 2, 3, 4, 6, 8, 12, 24.


Step Two: List the factors that they share:

Factors of 16 & 24: 1, 2, 4, 8.


Step Three: Find the largest factor which the two numbers have in common. In this case that number is 8. Sometimes the largest common factor for two numbers is 1, but most of the numbers you will be asked about will have larger common factors.

Here's another example: 

  Find the GCF of 20 and 40.

  STEP ONE: List all factors.

     Factors of 20: 1, 2, 4, 5, 10, 20.
     Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.

  STEP TWO: List all COMMON factors.

     Common Factors of 20 and 40: 1, 2, 4, 5, 10, 20.

  STEP THREE: Identify GREATEST COMMON FACTOR.

      GCF of 20 and 40: 20.
You can also find the GCF for more than two numbers. For instance:

GCF of 30, 12, and 42: 6.

You get to find some greatest common factors for yourself on the next page.

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