Problem 44747. Exponents in Factorials

Created by James

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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!</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>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.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>You can assume that both n and k are both integers greater than 1.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

70 Solutions
23 Solvers

Last Solution submitted on Mar 22, 2023

Last 200 Solutions

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!

Solution Comments

Show comments

Problem Recent Solvers23

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44747. Exponents in Factorials

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers23

Suggested Problems

More from this Author80

Problem Tags

Community Treasure Hunt

Problem 44747. Exponents in Factorials

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers23

Suggested Problems

More from this Author80

Problem Tags

Community Treasure Hunt

Players