What is the gcf of 64 and 72?

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 both numbers have in common.One way to determine the greatest common factor is to find all the factors of the numbers and compare them.
The factors of 64 are 1, 2, 4, 8, 16, 32, and 64.
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 greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.
The prime factors of 64 are 2, 2, 2, 2, 2, and 2.
The prime factors of 72 are 2, 2, 2, 3, and 3.
The prime factors in common are 2, 2, and 2, so the greatest common factor is 2 x 2 x 2 = 8.
SummaryA 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 both numbers have in common. 

Summary:
The common factors of 64 and 72 are 1, 2, 4, and 8.
The greatest common factor of 64 and 72 is 8.

Or in the short term; the answer is 8