P, q, and r are prime #'s and a, b, and c are positve intgers, how many divisors

[mr_coffee]

Hello everyone.

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.

 

[mattmns]

Yes, that looks good, except for one part. The answer should be (a+1)(b+1)(c+1). You wrote (r+1) instead of (c+1), but I think this was just a typo.

 

[mr_coffee]

ahh yes! thanks for picking that up, it was a typo.
Thanks for the responce.