Question

In how many ways can the number $7056$ be resolved into two factors?

Answer 1

$7056=2^4{\times 3}^2\times 7^2$

A number of form $a^p{b}^q{c}^r...$ where $a,b,c$ are all prime and $p,q,r$ are all even can be resolved in two factors in $\frac{1}{2}\left[\right(p+1\left)\right(q+1\left)\right(r+1)....+1]$ ways

So number of ways of resolving the number $=\frac{1}{2}\left\{\right(4+1\left)\right(2+1\left)\right(2+1)+1\}=\frac{46}{2}=23$