Question

The greatest common factor of a number n and 6 is 3. What are all of he possible whole-number values for n?

Answer 1

9, 21, 27, 33, 39, etc. just keep going up by 6

Answer 2

Answer: Odd multiple of 3.

`3,\ 9,\ 15,\ 21, \ 27, \ 33, \ 39,\ 45,...........`

Explanation:

Given : The greatest common factor of a number n and 6 is 3.

Then, it is clear that n should be a multiple of 3.

Prime factorization of 6 :

`6=2*3`

So for n a even number then the greatest common factor will be 6.

Thus , the possible choice for n is a odd multiple of 3.

Hence, the possible whole-number values for n are :

`3,\ 9,\ 15,\ 21, \ 27, \ 33, \ 39,\ 45,...........`