How many trailing zeros in 100!?

How many trailing zeros in 100!?

Approach: Count factors of 5 (since factors of 2 are more abundant).

24. Number of multiples of 5: ⌊100/5⌋=20. Plus multiples of 25: ⌊100/25⌋=4. Total = 20+4=24.

Follow-up: What about 1000!?

Key concepts: prime factors, floor division, trailing zeros.