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Math Help - How many divisors does the product have?

  1. #1
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    How many divisors does the product have?

    If p and q are prime numbers, how many divisors does the product p^3*q^6 have?

    Prime factorization would suggest that the answer is 18, but apparently it is 28. Please explain. Thanks.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: How many divisors does the product have?

    Quote Originally Posted by skyd171 View Post
    If p and q are prime numbers, how many divisors does the product p^3*q^6 have?

    Prime factorization would suggest that the answer is 18, but apparently it is 28. Please explain. Thanks.
    You forgot the cases 1,p,\cdots,p^3,q,\cdots,q^6. In general \sigma_0(p^nq^m)=(n+1)(m+1), recall that \sigma_0 is multiplicative and \sigma_0(p^n)=n+1.
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    Re: How many divisors does the product have?

    wonderful. Is it correct that the sigma, in this context, means "the number of unique divisors of"?
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Re: How many divisors does the product have?

    Quote Originally Posted by skyd171 View Post
    wonderful. Is it correct that the sigma, in this context, means "the number of unique divisors of"?
    I don't know what unique divisor means, but it is the number of divisors, it is a special case of the more general divisor function.
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