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Math Help - How many positive integers divide 3^3*5^5*7^7

  1. #1
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    How many positive integers divide 3^3*5^5*7^7

    Hi,

    I have been told that the following problem is very easy to solve, but I have no clue how to do it apart from trial and error, which would take ages. It says:

    "Find how many different positive integers divide

    3^3*5^6*7^7"

    Thanks in advance for any help you can give me
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  2. #2
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    Suppose there are four primes, p,~q,~r~\&~s and each of a,~b,~ c,~ \&~ d is a non-negative integer then the number of factors p^a\cdot q^b\cdot r^c\cdot s^d\cdot is (a+1) (b+1) (c+1) (d+1) .
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