Problem 42510. Divisible by n, Composite Divisors

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{"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>.

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Last Solution submitted on Mar 21, 2023

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Jonathan on 11 Jan 2020

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

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Problem 42510. Divisible by n, Composite Divisors

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