Problem 42455. Divisible by n, prime divisors - 11, 13, 17, & 19

Created by goc3

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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>Divisibility checks against prime numbers can all be accomplished with the same routine, applied recursively, consisting of add or subtract x times the last digit to or from the remaining number. For example, for 13, add four times the last digit to the rest:</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>2392: 239 + 4*2 = 247: 24 + 4*7 = 52: 5 + 4*2 = 13 -&gt; 2392 is divisible by 13.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For 17, subtract five times the last digit from the rest:</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>3281: 328 - 5*1 = 323: 32 - 5*3 = 17 -&gt; 3281 is divisible by 17.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For 19, add two times the last digit to the rest:</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>16863: 1686 + 2*3 = 1692: 169 + 2*2 = 173: 17 + 2*3 = 23: 2 + 2*3 = 8 -&gt; 16863 is not divisible by 19.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>And, for 11, subtract the last digit from the rest:</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>269830: 26983 - 0 = 26983: 2698 - 3 = 2695: 269 - 5 = 264: 26 - 4 = 22: 2 - 2 = 0 -&gt; 269830 is divisible by 11.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function to return a true-false vector for the prime numbers in the 11:20 range ([11 13 17 19]) based on a number supplied as a string.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Restrictions on Java, mod, ceil, round, and floor are still in effect.</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/42454-divisible-by-n-prime-divisors-including-powers\"><w:r><w:t>Divisible by n, prime divisors (including powers)</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/42508-divisible-by-n-prime-divisors-from-20-to-200\"><w:r><w:t>Divisible by n, prime divisors from 20 to 200</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>"}]}

Divisibility checks against prime numbers can all be accomplished with the same routine, applied recursively, consisting of add or subtract x times the last digit to or from the remaining number. For example, for 13, add four times the last digit to the rest:<ul><li>2392: 239 + 4*2 = 247: 24 + 4*7 = 52: 5 + 4*2 = 13 -&gt; 2392 is divisible by 13.</li></ul>For 17, subtract five times the last digit from the rest:<ul><li>3281: 328 - 5*1 = 323: 32 - 5*3 = 17 -&gt; 3281 is divisible by 17.</li></ul>For 19, add two times the last digit to the rest:<ul><li>16863: 1686 + 2*3 = 1692: 169 + 2*2 = 173: 17 + 2*3 = 23: 2 + 2*3 = 8 -&gt; 16863 is not divisible by 19.</li></ul>And, for 11, subtract the last digit from the rest:<ul><li>269830: 26983 - 0 = 26983: 2698 - 3 = 2695: 269 - 5 = 264: 26 - 4 = 22: 2 - 2 = 0 -&gt; 269830 is divisible by 11.</li></ul>Write a function to return a true-false vector for the prime numbers in the 11:20 range ([11 13 17 19]) based on a number supplied as a string.Restrictions on Java, mod, ceil, round, and floor are still in effect.Previous problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42454-divisible-by-n-prime-divisors-including-powers">Divisible by n, prime divisors (including powers)</a>. Next problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42508-divisible-by-n-prime-divisors-from-20-to-200">Divisible by n, prime divisors from 20 to 200</a>.

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Last Solution submitted on Dec 01, 2020

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2 Comments

bainhome on 9 May 2018

in problem's explantation, Example in "17" part, it probably is: "3281 is divisible by 17.", not 2392 ?

goc3 on 10 May 2018

@bainhome: thanks for catching that; it's been fixed.

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Problem 42455. Divisible by n, prime divisors - 11, 13, 17, & 19

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Problem 42455. Divisible by n, prime divisors - 11, 13, 17, & 19

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