Problem 44068. The number of trailing zero digit of a factorial

Created by Jihye Sofia Seo

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For given positive integer n, take factorial of that number. How many trailing zeros does it have?

Example: factorial(11) = 39916800

Its last zero-digit count is 2.

Optional: Can you make an efficient algorithm for a very large n?

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Last Solution submitted on Feb 13, 2025

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HighPhi on 20 Jul 2020

vpa(factorial(27)) = 10888869450418351940239884288

...
no trailing zeros
factorial(27) = 1.088886945041835e+28
...

vpa(factorial(27)) - 1.088886945041835e+28 - 2.199023255552000e+12 = 0

I don't get it.
if vpa(factorial) = 10888869450418351940239884288
then there are no trailing zeros...

vpa(factorial(11)) = 39916800
two trailing, like in your problem statement...

am I crazy?

ChrisR on 23 Jul 2020

Highphi, any factorial equal to or greater than 5! has to have trailing zeros because it will have one or more pairs of 2 and 5 in its factors. I think factorial(vpa(27)) will give the correct value.

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Problem 44068. The number of trailing zero digit of a factorial

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Problem 44068. The number of trailing zero digit of a factorial

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