Since p and q are unique primes, every factor of r must be a product of some number of p's and some number of q's. A given factor of r can have anywhere between 0 p's in it and m p's in it. Likewise, it can have between 0 q's and n q's.

You can either use some combinatoric methods or write it out in general in a table and count them up. Consider to denote the number of M's and number of N's in a factor. Then one factor is (0,1), which respresents . Another is (0,2). Can you count them all up from there?