CodingMediumcod-g828

Subject Number theoryLevel Mid–Senior~15 minCommon in Algorithms & data structures interviewsIndustries Software development

Question

Return the number of trailing zeros in n factorial (n!) without computing the factorial itself, for n up to 10^9. A trailing zero comes from a factor of 10 = 2 * 5, and fives are scarcer than twos, so count the multiplicity of 5 in n! using Legendre's formula: floor(n/5) + floor(n/25) + floor(n/125) + ... Return 0 for n < 0.

Implement

factorial_trailing_zeros(n: int) → int

Examples

in[25]out6

What a strong answer looks like

State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.

Learn the concepts

Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.

Run or narrate your approach, then ask the coach.