Is it possible to find the digit sum of $n!$ ($n \in \mathbb{N} \text{ and } n \le100$) without actually computing the factorial?
I faced this problem in quantitative aptitude test which asks to find the sum of the digits of $25!$, I was wondering if there is any paper pencil approach to deduce the sum from counting the number of each digits in the factorial without actually computing the whole thing.