If m and n are positive integers such that the greatest common factor of and is 45, then which of the following could n equal?
(a) 3
(b) 5
(c) 9
(d) 15
(e) 45

The greatest common factor of  and 

is
 
gcd(m*m*n*n, m*n*n*n) =m*n*n=

what we did, was to see how many m's and how many n's, each expression have, and then pick the smallest of each letter (factor).

the reason is that the common factor, must have enough m's and n's to divide the m's and n's of both expressions

so

also 


thus, n is equal to 3

A)3