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

  1. Oct 21, 2006 #1
    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 any one of the a+1 numbers listed above times any one 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.
     
  2. jcsd
  3. Oct 21, 2006 #2
    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.
     
  4. Oct 21, 2006 #3
    ahh yes! thanks for picking that up, it was a typo.
    Thanks for the responce.
     
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