What is the greatest common factor of 64 and 114?

Answer 1

The greatest common factor of 64 and 114 is 2.

The common factors of 64 and 114 are 1 and 2.

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

Methods:

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 64 are 1, 2, 4, 8, 16, 32, and 64.

The factors of 114 are 1, 2, 3, 6, 19, 38, 57, and 114.

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

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 114 are 2, 3, and 19.

The prime factors in common are a single 2, so the greatest common factor is 2.
Factors of 64: 1, 2, 4, 8, 16, 32, 64

Factors of 114: 1, 2, 3, 6, 19, 38, 57, 114

GCF (64, 114) = 2

Answer 2

Greatest common factor of 64 and 114 is 2.