Solution
Trailing Zeros
Show the problem again
How many zeros does 100! (100 factorial) end in?
Worked solution
The answer is 24. Trailing zeros come from factors of 10 = 2 × 5, and factors of 5 are scarcer than 2s. Count multiples of 5 in 1–100: ⌊100/5⌋ = 20, plus extra fives from multiples of 25: ⌊100/25⌋ = 4. Total: 20 + 4 = 24 trailing zeros.
Source: Application of Legendre's formula (1808); standard number-theory exercise. Statement written for AxiomIQ.