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

Created by Jihye Sofia Seo

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For given positive integer n, its factorial often has many trailing zeros, in other words many factors of 10s. In order for n! to have at least "m" trailing zeros, what is the smallest "n" ?

Example: factorial(10) = 3628800 factorial(9) = 362880 In order to have 2 trailing zeros on factorial, the smallest n is 10.

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

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Last Solution submitted on Nov 22, 2019

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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

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

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Last 200 Solutions

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Problem Recent Solvers13

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

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Last 200 Solutions

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Problem Recent Solvers13

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