## Factorial digit sum

### Problem 20

Published on Friday, 21st June 2002, 06:00 pm; Solved by 121458; Difficulty rating: 5%*n*! means *n* × (*n* − 1) × ... × 3 × 2 × 1

For example, 10! = 10 × 9 × ... × 3 × 2 × 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!