What is the greatest common factor of 7 and 21?

Answer 1

The GCF of 7 and 21 is 7. Since 7 is a factor of 21, it is automatically the GCF.

Definition: A factor is a divisor - a number that will evenly divide into another number. The greatest common factor of two or more numbers is the largest factor that the numbers have in common.

Method:

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 7 are 1 and 7.

The factors of 21 are 1, 3, 7, and 21..

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

Answer 2

The set of factors of 21 = {1, 3, 7, 21}

Comparatively, the set of factors of 7 (owing to the fact that it is a Prime number), = {1, 7}.

Therefore, taking the union of these two sets and looking at its max will give us the highest common factor of the two. The union of these two sets = {1, 7}, which implies that the highest common factor of 21 and 7 = 7.