What is the greatest common factor of 75 and 120?

Answer 1

Answer: 15

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 75 are 1, 3, 5, 15, 25, and 75.

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

The common factors are 1, 3, 5, and 15. Therefore, the greatest common factor is 15.
The factors of 75 are:

1, 3, 5, 15, 25, 75

The factors of 120 are:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

The common factors are:

1, 3, 5, 15

The Greatest Common Factor (GCF) is:

15