What is the greatest common factor of 70 and 100?

Answer 1

The greatest common factor of 70 and 100 is 10.

The common factors of 70 and 100 are 1, 2, 5, and 10.

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 70 are 1, 2, 5, 7, 10, 14, 35, and 70.

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.

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

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

The prime factors of 70 are 2, 5, and 7.

The prime factors of 100 are 2, 2, 5, and 5.

The prime factors in common are 2 and 5, so the greatest common factor is 2 x 5 = 10.

Still another way is to recognize that both numbers are divisible by 10 since they both end in 0. Then, divide both numbers by 10 and compare the results.

70 ÷ 10 = 7

100 ÷ 10 = 10

Since 7 and 10 do not have any factors in common, the greatest common factor is 10.