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Factoring and Multiples

# What is the greatest common factor of 32 and 72?

###### 12/02/2017

The greatest common factor of 32 and 72 is 8.

Definition: A factor is a divisor - a number that will evenly divide into another number. The greatest common factor of two or more numbers is the largest factor that the numbers have in common.

Method:

One way to determine the common factors and greatest common factor is to find all the factors of the numbers and compare them.

The factors of 32 are 1, 2, 4, 8, 16, and 32.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

The common factors are 1, 2, 4, and 8. Therefore, the greatest common factor is 8.

The factors of 32 are 1, 2, 4, 8, 16, and 32.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

The largest of the factors they have in common is 8, so 8 is the greatest common factor.

Using the prime factorization method:

The prime factors of 32 are 2, 2, 2, 2, and 2.

The prime factors of 72 are 2, 2, 2, 3, and 3.

The prime factors they have in common are 2, 2, and 2, so the greatest common factor is 2 x 2 x 2 = 8.
GCF=8
The GCF is 8.
The Greatest Common Factor is 8

GCF(32, 72) = 8.