Identify the GCF

Now that you have refreshed your memory of finding factors, let’s move on to finding the greatest common factor for a set of numbers. Review the slides to learn more about finding the GCF of a set of numbers.

Number 16 next to the number twenty four.

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Factors First!

Before you can determine the GCF for a set of numbers, you need to identify the factors of each number you are working with. Consider the numbers 16 and 24.

The factors of each number are shown here:
16: 1, 2, 4, 8, 16
24: 1, 2, 3, 4, 6, 8, 12, 24

Common Factors

Now that you have identified the factors for each number individually, it is time to see what they have in common.

Common means “alike.” A “common factor” is a factor that is the same between two or more numbers. For example, 5 is a common factor for both 25 and 30; this is because both 25 and 30 can be divided evenly by 5.

Now, review the factors for 16 and 24 and mark any factors that are the same, like this:
16: 1, 2, 4, 8,16
24: 1, 2, 3, 4, 6, 8, 12, 24
16 and 24 share the factors of 1, 2, 4, and 8.

Greatest Common Factor

Once you have identified all of the factors that two or more numbers have in common, you can compare them to see which common factor is the greatest. In math, “greatest” means the largest.

The common factor that has the greatest value will be the greatest common factor.
Notice that 16 and 24 share the factors 1, 2, 4, and 8.

The greatest factor that 16 and 24 have in common is 8. This means that the GCF of 16 and 24 is 8.

Your turn! For each set of numbers below, list their factors and determine which one is the GCF. Click the row to check your work.

14 and 28

Factors of 14: 1, 2, 7, 14
Factors of 28: 1, 2, 4, 7, 14, 28
Common factors for 14 and 28: 1, 2, 7, 14
GCF of 14 and 28: 14

12 and 22

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 22: 1, 2, 11, 22
Common factors for 12 and 22: 1, 2
GCF of 12 and 22: 2

30 and 50

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 50: 1, 2, 5, 10, 25, 50
Common factors for 30 and 50: 1, 2, 5, 10
GCF of 30 and 50: 10

27 and 36

Factors of 27: 1, 3, 9, 27
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors for 27 and 36: 1, 3, 9
GCF of 27 and 36: 9

42 and 56

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Common factors for 42 and 56: 1, 2, 7, 14
GCF of 42 and 56: 14

Learning Coach — Greatest Common Factors

Objectives

Skills Needed

Keywords

Learning Coach Notes

Identify the GCF

How do you identify the GCF for a set of numbers?

Factors First!

Common Factors

Greatest Common Factor