Problem 44747. Exponents in Factorials

Created by James
Appears in Physics

Difficulty:Rate

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It's time to get excited about numbers!!! Well, we're just dealing with factorials here, but it's still a good reason to get excited. You're given two numbers, n and k. Calculate the highest exponent of k that could appear in n!

For example, for n=5 and k=2, you're looking for the highest exponent of 2 that could appear in 5!, or 120. The highest power of 2 that evenly divides 120 is 3 (2^3 evenly divides 120, while 2^4 does not) so your output for maxexp(5,2)=3.

You can assume that both n and k are both integers greater than 1.

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Solution Stats

79 Solutions
26 Solvers

Last Solution submitted on Jul 28, 2024

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Problem Comments

2 Comments

2 Comments

li haitao on 23 Oct 2018

Please add test cases:
assert(isequal(maxexp(1e9, 2), 999999987))
assert(isequal(maxexp(1e9, 3), 499999993))

James on 23 Oct 2018

The harder test cases were going to be in version 2 of the problem. This was just to get the ball rolling. I see that you went ahead and submitted the problem with your added test cases, which is never a bad thing. Thanks, and I'm glad you liked the problem!