- #1

mr_coffee

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I think i got this right but i want to make sure...

If p, q and r are prime numbers and a, b, and c are positive integers, how many possible divisors does p^a*p^b*r^c have?

I said...

There are a+1 divisors: 1, p, p^2...,p^a

A divisor is a product of anyone of the a+1 numbers listed above times anyone of the b+1 numbers 1, q, q^2...q^b. We also have r+1...1, r, r^2...,r^c so by the muliplication rule, there are (a+1)(b+1)(r+1) divisors in all.