What is the greatest common factor of 40 and 700?

Answer 1

The GCF of 40 and 700 is 20.

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

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

The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, and 700.

The common factors are 1, 2, 4, 5, 10, and 20. Therefore, the greatest common factor is 20.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.

The prime factors of 40 are 2, 2, 2, and 5 (which can also be represented as 23 and 5).

The prime factors of 700 are 2, 2, 5, 5, and 7 (which can also be represented as 22, 52, and 7).

The prime factors in common are 2, 2, and 5, so the greatest common factor is 2 x 2 x 5 = 20.

This is a situation in which you could also make a reasonable guess and then refine it. Both 700 and 40 are divisible by 10, since they end in 0. So, divide both by 10 and then check whether they have additional common factors.

700 ÷ 10 = 70

40 ÷ 10 = 4

Both results are even, so divide the results by 2.

70 ÷ 2 = 35

4 ÷ 2 = 2

There is not an additional number that will divide the results, so we have 10 and 2, which means the greatest common factor is 10 x 2 = 20.