020 - Factorial Digit Sum

Problem 20 / Challenge #20: Factorial Digit Sum

$n!$ means $n \times (n - 1) \times \cdots \times 3 \times 2 \times 1$.

For example, $10! = 10 \times 9 \times \cdots \times 3 \times 2 \times 1 = 3628800$,
and the sum of the digits in the number $10!$ is $3 + 6 + 2 + 8 + 8 + 0 + 0 = 27$.

Find the sum of the digits in the number $100!$.

ProjectEuler+ Problem Statement

The Project Euler problem is equivalent to the ProjectEuler+ challenge with $T = 1$ and $N = 100$.