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

76 Solutions
41 Solvers

Last Solution submitted on Sep 09, 2020

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 Solvers41

Problem Tags

factorial integer number theory power of tens

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

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers41

Suggested Problems

More from this Author9

Problem Tags

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

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers41

Suggested Problems

More from this Author9

Problem Tags

Players