Problem 42510. Divisible by n, Composite Divisors

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>Pursuant to</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>, this problem requires you to write a function that determines divisibility for a large number (n_str) when the divisor is a composite. As was required in that problem, you will need to formulate the highest-power factorization of the divisor. Divisibility of n_str can then be determined by testing against each highest-power factor. For simplicity, this problem is restricted to numbers that contain the following as highest-power factors: 2, 3, 4, 5, 8, 9, and 10, as these divisibility tests are trivial. Their rules are included briefly below, for reference.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>As an example, a number is divisible by 30 if it is divisible by 2, 3, and 5, as those are the highest-power factors for 30. Likewise, a number is divisible by 36 if it is divisible by 4 and 9 (not 3), as those are its highest-power factors.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The only restriction that remains is Java.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Divisible by 2: if the last digit is divisible by 2.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Divisible by 3: if the sum of the number's digits (n_str) is divisible by 3. Apply iteratively, as necessary, to arrive at a single-digit number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Divisible by 4: if the last two digits are divisible by 4.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Divisible by 5: if the last digit is a 0 or 5.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Divisible by 8: if the last three digits are divisible by 8.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Divisible by 9: if the sum of the number's digits (n_str) is divisible by 9. Apply iteratively, as necessary, to arrive at a single-digit number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Divisible by 10: if the last digit is zero.</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/42509-divisible-by-n-truncated-number-divisors\"><w:r><w:t>Divisible by n, Truncated-number 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>"}]}

Pursuant to <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>, this problem requires you to write a function that determines divisibility for a large number (n_str) when the divisor is a composite. As was required in that problem, you will need to formulate the highest-power factorization of the divisor. Divisibility of n_str can then be determined by testing against each highest-power factor. For simplicity, this problem is restricted to numbers that contain the following as highest-power factors: 2, 3, 4, 5, 8, 9, and 10, as these divisibility tests are trivial. Their rules are included briefly below, for reference.As an example, a number is divisible by 30 if it is divisible by 2, 3, and 5, as those are the highest-power factors for 30. Likewise, a number is divisible by 36 if it is divisible by 4 and 9 (not 3), as those are its highest-power factors.The only restriction that remains is Java.<ul><li>Divisible by 2: if the last digit is divisible by 2.</li><li>Divisible by 3: if the sum of the number's digits (n_str) is divisible by 3. Apply iteratively, as necessary, to arrive at a single-digit number.</li><li>Divisible by 4: if the last two digits are divisible by 4.</li><li>Divisible by 5: if the last digit is a 0 or 5.</li><li>Divisible by 8: if the last three digits are divisible by 8.</li><li>Divisible by 9: if the sum of the number's digits (n_str) is divisible by 9. Apply iteratively, as necessary, to arrive at a single-digit number.</li><li>Divisible by 10: if the last digit is zero.</li></ul>Previous problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42509-divisible-by-n-truncated-number-divisors">Divisible by n, Truncated-number Divisors</a>.

Pursuant to <http://www.mathworks.com/matlabcentral/cody/problems/42453-divisible-by-n-prime-vs-composite-divisors Divisible by n, prime vs. composite divisors>, this problem requires you to write a function that determines divisibility for a large number (n_str) when the divisor is a composite. As was required in that problem, you will need to formulate the highest-power factorization of the divisor. Divisibility of n_str can then be determined by testing against each highest-power factor. For simplicity, this problem is restricted to numbers that contain the following as highest-power factors: 2, 3, 4, 5, 8, 9, and 10, as these divisibility tests are trivial. Their rules are included briefly below, for reference.

As an example, a number is divisible by 30 if it is divisible by 2, 3, and 5, as those are the highest-power factors for 30. Likewise, a number is divisible by 36 if it is divisible by 4 and 9 (not 3), as those are its highest-power factors.

The only restriction that remains is Java.

* Divisible by 2: if the last digit is divisible by 2.
* Divisible by 3: if the sum of the number's digits (n_str) is divisible by 3. Apply iteratively, as necessary, to arrive at a single-digit number.
* Divisible by 4: if the last two digits are divisible by 4.
* Divisible by 5: if the last digit is a 0 or 5.
* Divisible by 8: if the last three digits are divisible by 8.
* Divisible by 9: if the sum of the number's digits (n_str) is divisible by 9. Apply iteratively, as necessary, to arrive at a single-digit number.
* Divisible by 10: if the last digit is zero.

Previous problem: <http://www.mathworks.com/matlabcentral/cody/problems/42509-divisible-by-n-truncated-number-divisors Divisible by n, Truncated-number Divisors>.

Solve

Solution Stats

133 Solutions
64 Solvers

Last Solution submitted on May 18, 2022

Last 200 Solutions

Solution Comments

Solution 2089110

1 Comment

1 Comment

Jonathan on 11 Jan 2020

I got tired of solving these problems. So, I just wrote a solution that works for everything.

Problem Recent Solvers64

Problem Tags

divisibility divisible divisor overflow precision prime string

Community Treasure Hunt

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

Start Hunting!

Problem 42510. Divisible by n, Composite Divisors

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers64

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Problem 42510. Divisible by n, Composite Divisors

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers64

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players