Problem 44071. Smallest n, for n! to have m trailing zero digits

Created by Jihye Sofia Seo

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Last Solution submitted on May 03, 2022

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Solution 1135219

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yurenchu on 7 Mar 2017

I think this is (so far) the most efficient solution for large m. It requires at most log(4*m)/log(5) iterations; while the smaller sized solutions that have been suggested require at least 0.8*m iterations (or a very large array). For example, for m = 10^5, this solution takes at most 8 iterations while the other solutions of smaller size require at least 80,000 iterations.

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factorial factorisation integer power of primes

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Problem 44071. Smallest n, for n! to have m trailing zero digits

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Problem 44071. Smallest n, for n! to have m trailing zero digits

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