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

Created by Jihye Sofia Seo

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>For given positive integer n, take factorial of that number. How many trailing zeros does it have?</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>Example: factorial(11) = 39916800</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>Its last zero-digit count is 2.</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>Optional: Can you make an efficient algorithm for a very large n?</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

120 Solutions
47 Solvers

Last Solution submitted on Jun 07, 2021

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

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.

Problem Recent Solvers47

Problem Tags

factorial integer number theory power of tens

Community Treasure Hunt

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

Start Hunting!

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

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers47

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

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

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers47

Suggested Problems

More from this Author9

Problem Tags

Community Treasure Hunt

Players