How many trailing zeros in 100 factorial?

How many trailing zeros in 100 factorial?

Approach: Count the number of factors of 5 in the prime factorization.

24. 100/5 = 20. 100/25 = 4. 20 + 4 = 24.

Follow-up: How many trailing zeros in 50 factorial?

Key concepts: Legendre's formula, prime factorization.