What is the greatest common factor of 80 and 72?

Answer 1

One way to approach this is to look at the difference between 72 and 80, which is 8. The greatest common factor of two numbers cannot be larger than the difference between the two numbers. Since both 72 and 80 are divisible by 8, the greatest common factor is 8.

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

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

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

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 72 are 2, 2, 2, 3, and 3.

The prime factors of 80 are 2, 2, 2, 2, and 5.

The prime factors in common are 2, 2, and 2, so the greatest common factor is 2 x 2 x 2 = 8.

Answer 2

The greatest common factor of 80 and 72 is 8.