# Definition of Greatest Common FactorSupport Page

Welcome to our Definition of Greatest Common Factor page.

As well as a clear definition of the greatest common factor we have links to our Greatest Common Factor calculator and also our Greatest Common Factor worksheets pages.

The Greatest Common Factor is also sometimes called the Highest Common Factor.

## Definition of Greatest Common Factor

### Examples

Example 1) Find the greatest common factor of 24 and 32.

We list the factors of both numbers:

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 32: 1, 2, 4, 8, 16, 32

The common factors of 24 and 32 are: 1, 2, 4, and 8.

The Greatest Common Factor is 8.

Example 2) Find the greatest common factor of 60 and 48.

We list the factors of both numbers:

• Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
• Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The common factors of 60 and 48 are: 1, 2, 3, 4, 6, and 12.

The Greatest Common Factor is 12.

Example 3) Find the greatest common factor of 35 and 22.

We list the factors of both numbers:

• Factors of 35: 1, 5, 7, 35
• Factors of 22: 1, 2, 11, 22

The only common factor of 35 and 22 is 1.

The Greatest Common Factor is 1. This means that the two numbers are coprime.

Example 4) Find the greatest common factor of 39 and 13.

We list the factors of both numbers:

• Factors of 39: 1, 3, 13, 39
• Factors of 13: 1, 13 (this number is prime)

The common factors of 39 and 13 are 1 and 13.

The Greatest Common Factor is 13.

Note that it is fine for the greatest common factor to be one of the numbers you are testing, if the other number is a multiple of it like in the example shown.

### Examples

Example 1) Find the greatest common factor of 30 and 45.

As a product of prime numbers:

• 30 = 2 x 3 x 5
• 45 = 3 x 3 x 5

We can see that the repeated part of the product in both lists is: 3 x 5.

The Greatest Common Factor is 3 x 5 = 15.

Example 2) Find the greatest common factor of 42 and 27.

As a product of prime numbers:

• 42 = 2 x 3 x 7
• 27 = 3 x 3 x 3

We can see that the repeated part of the product in both lists is: 3.

The Greatest Common Factor is 3.

Example 3) Find the greatest common factor of 88 and 45.

As a product of prime numbers:

• 88 = 2 x 2 x 2 x 11
• 45 = 3 x 3 x 5

We can see that there are no repeated factors in both lists.

The Greatest Common Factor is 1.

Example 4) Find the greatest common factor of 24, 18 and 42.

As a product of prime numbers:

• 24 = 2 x 2 x 2 x 3
• 18 = 2 x 3 x 3
• 42 = 2 x 3 x 7

We can see that the repeated part of the product in both lists is: 2 x 3.

The Greatest Common Factor is 2 x 3 = 6.

### More Recommended Math Worksheets

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### Prime Factorization Worksheets

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