Let p, q and r be distinct odd primes. Suppose n = pq and m = pr. Given that you know that m and n share a common prime factor, but that you do not know the values of p, q, r, explain how you may obtain the prime factors of m and n without using the method of prime factorization?
Can someone help me start this?
Hint: What's the greatest common divisor of $m$ and $n$?