What is the greatest common factor of 70 and 84?

Answer 1

The GCF of 70 and 84 is 14.

One way to approach this is to look at the difference between 70 and 84, which is 14. 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. Since both 70 and 84 are divisible by 14, the greatest common factor is 14.

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 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

The common factors are 1, 2, 7, and 14. Therefore, the greatest common factor is 14.

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 84 are 2, 2, 3, and 7.

The prime factors in common are 2 and 7, so the greatest common factor is 2 x 7 = 14. 14