What is the greatest common factor of 70 and 90?

Answer 1

The GCF of 70 and 90 is 10.

One way to approach this is to look at the difference between 70 and 90, which is 20. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference. Neither 70 nor 90 are divisible by 20, so look at the next largest factor of 20, which is 10. Both 70 and 90 are divisible by 10, so the greatest common factor is 10.

Another way to determine the 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 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

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 90 are 2, 3, 3, and 5.

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