CAT (QA) PYQs

If $m$ and $n$ are natural numbers such that $n > 1$, and $m^{n}=2^{25} \times 3^{40}$, then $m-n$ equals

How many factors of $2^4 \times 3^5 \times 10^4$ are perfect squares which are greater than $1?$

The sum of the first two natural numbers, each having $15$ factors (including $1$ and the number itself), is