Problem 42418. Divisible by 16

Created by goc3

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","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\"?>\n<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>Write a function to determine if a number is divisible by 16. This can be done by a few different methods. Here are two:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>If a number has four or more digits, take the last three digits. Add eight to it if the thousands digit in the original number is odd (zero if even). If this three-digit number is divisible by 16, so is the original number. The resulting number can also be reduced by the following method.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>Take the last two digits and add them to four times the remaining number. Apply this method recursively until a two-digit number remains. As usual, if the resulting number is divisible by 16, then so is the original number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A few of the function restrictions have been lifted.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Previous problem:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42417-divisible-by-15\"><w:r><w:t>divisible by 15</w:t></w:r></w:hyperlink><w:r><w:t>. Next problem:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42453-divisible-by-n-prime-vs-composite-divisors\"><w:r><w:t>divisible by n, prime vs. composite divisors</w:t></w:r></w:hyperlink><w:r><w:t>.</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>"}]}

Write a function to determine if a number is divisible by 16. This can be done by a few different methods. Here are two:<ol><li>If a number has four or more digits, take the last three digits. Add eight to it if the thousands digit in the original number is odd (zero if even). If this three-digit number is divisible by 16, so is the original number. The resulting number can also be reduced by the following method.</li><li>Take the last two digits and add them to four times the remaining number. Apply this method recursively until a two-digit number remains. As usual, if the resulting number is divisible by 16, then so is the original number.</li></ol>A few of the function restrictions have been lifted.Previous problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42417-divisible-by-15">divisible by 15</a>. Next problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42453-divisible-by-n-prime-vs-composite-divisors">divisible by n, prime vs. composite divisors</a>.

Solve

Solution Stats

491 Solutions
163 Solvers

Last Solution submitted on May 07, 2023

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

James on 29 Jun 2015

Another trick: if the last 4 digits of the number are divisible by 16, the full number is divisible by 16. So far as I know, if the last X digits of a number are divisible by 2^X, the entire number is divisible by 2^X.

Alfonso Nieto-Castanon on 29 Jun 2015

@James: nice trick! (and I guess the proof arises from 10^x being always exactly divisible by 2^x, so "iff" also applies?)

Alfonso Nieto-Castanon on 29 Jun 2015

perhaps less interesting but I guess you could do the same with powers of 5, iff the last X digits of a number are divisible by 5^x, then the entire number is divisible by 5^x...

Solution Comments

Show comments

Problem Recent Solvers163

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 42418. Divisible by 16

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers163

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 42418. Divisible by 16

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers163

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players