If a and b are nonzero whole numbers and a is a factor of b, what is the GCF of aand b? Explain your thinking and give three numerical examples to support your answer.

In this, simply use the concept of GCF by finding the prime factor.

Since, it is known thatif a is a factor of b, then the GCF between the two numbers will be a. This is because, as ‘a’ is a factor of ‘b’, then ‘a’ cannot have a factor which is greater than itself.

To prove this, Let’s take three example which proves this situation,

Example I :-

Assume: $a=6,b=42$

The factor of$6$: $6=1,2,3,6$

The factor of $42$: $42=1,2,3,6,7,14,21,42$

The greatest common factor is \[6\] which is ‘a’.

Example II :-

Assume: $a=8,b=42$

The factor of$8$: 8=1,2,4,8

The factor of42 : 42=1,2,3,6,7,14,21,42

The greatest common factor is 8 which is ‘a’.

Example III :-

Assume: a=7,b=42

The factor of 7 : 7=1,7

The factor of 42 : 42=1,2,3,6,7,14,21,42

The greatest common factor is 7 which is ‘a’.

Hence, it is clearly seen from the above that in all cases a is the factor of a and b.