The only common factor between these two numbers will be 1.
Remember that any number can be decomposed as a product of prime numbers. For example for 18 we have:
18 = 2*3*3
There 18 is written as a product of its prime factors.
Now, for our case of p^n and q^m we will have:
p^n = P = p*p*p...*p n times.
q^m = Q = q*q*q*...*q m times.
Now, notice that because q and p are primes, there is no common factor in these two decompositions. (and we can't decompose it furthermore). Then we conclude that the only factor that these numbers share is the trivial one, which is 1.
If you want to learn more about prime numbers, you can read:
https://brainly.com/question/145452
