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

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>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>.

Solve

Solution Stats

128 Solutions
42 Solvers

Last Solution submitted on Oct 23, 2020

Last 200 Solutions

Problem Comments

2 Comments

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.

Problem Recent Solvers42

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

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers42

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

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

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers42

Suggested Problems

More from this Author139

Problem Tags

Community Treasure Hunt

Players