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Zeros in factorial calculator

Enter n and get the count of trailing zeros in n factorial, computed with the Legendre divisor shortcut instead of building the factorial itself.

Enter n to count the zeros.

Every trailing zero of n! is one factor of 10, which needs a factor of 2 and a factor of 5 paired together. Twos are plentiful, so the fives decide the count, and the Legendre shortcut adds up how many times 5, 25, 125 and so on divide into n. That sum is the answer, computed in this tab without ever building n! itself, which is why n of a billion answers instantly and exactly. One honest boundary: this counts trailing zeros only, not the zeros in the middle of the number, and it cannot show you the digits of n!, which for large n would not fit in any memory.
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