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

1. ## 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

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

2. 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 $(a+1) (b+1) (c+1) (d+1)$.