Problem 42409. Divisible by 7

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>Pursuant to the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/42404-divisible-by-2\"><w:r><w:t>first problem</w:t></w:r></w:hyperlink><w:r><w:t> in this series, this one involves checking for divisibility by 7.</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 determine if a number is divisible by 7. This can be done by a variety of methods. Some are:</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>Multiply each digit in the candidate number (from right to left) by the digit in the corresponding position in this pattern: 1, 3, 2, -1, -3, -2 (1 applies to the ones digit, 3 to the tens digit, etc.). This pattern should be repeated beyond the hundred-thousands digit. The resulting sum will be a smaller number. This method can be applied recursively to the absolute values of the resulting sum until a single digit results. Then, check that number for divisibility by seven.</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>The previous method can also be used applying a slightly different pattern: 1, 3, 2, 6, 4, 5 (1 applies to the ones digit again, etc.). The absolute value of the resulting sum is not necessary as none of the factors are negative.</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>Multiply the last (ones) digit by two and subtract the result from the remaining number. Apply recursively, as noted in methods above.</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>Similar to the previous method, multiply the last digit by five and add to the remaining number. Apply recursively, as noted in methods above.</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>Double the last digit and subtract it from the remaining number (original number except for the ones digit). Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.</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>Similar to the previous method, multiply the ones digit by five and add it to the remaining number. Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.</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>Along similar lines, take the last three digits of the number and subtract that number from the remaining number. Once you reach a number less than 1000, another method can be applied to further reduce the number to check for divisibility by seven.</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>Etc. (there are others)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The restriction for multiplication has been lifted for this specific problem.</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/42408-divisible-by-6\"><w:r><w:t>divisible by 6</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/42410-divisible-by-8\"><w:r><w:t>divisible by 8</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 the <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42404-divisible-by-2">first problem</a> in this series, this one involves checking for divisibility by 7.Write a function to determine if a number is divisible by 7. This can be done by a variety of methods. Some are:<ol><li>Multiply each digit in the candidate number (from right to left) by the digit in the corresponding position in this pattern: 1, 3, 2, -1, -3, -2 (1 applies to the ones digit, 3 to the tens digit, etc.). This pattern should be repeated beyond the hundred-thousands digit. The resulting sum will be a smaller number. This method can be applied recursively to the absolute values of the resulting sum until a single digit results. Then, check that number for divisibility by seven.</li><li>The previous method can also be used applying a slightly different pattern: 1, 3, 2, 6, 4, 5 (1 applies to the ones digit again, etc.). The absolute value of the resulting sum is not necessary as none of the factors are negative.</li><li>Multiply the last (ones) digit by two and subtract the result from the remaining number. Apply recursively, as noted in methods above.</li><li>Similar to the previous method, multiply the last digit by five and add to the remaining number. Apply recursively, as noted in methods above.</li><li>Double the last digit and subtract it from the remaining number (original number except for the ones digit). Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.</li><li>Similar to the previous method, multiply the ones digit by five and add it to the remaining number. Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.</li><li>Along similar lines, take the last three digits of the number and subtract that number from the remaining number. Once you reach a number less than 1000, another method can be applied to further reduce the number to check for divisibility by seven.</li><li>Etc. (there are others)</li></ol>The restriction for multiplication has been lifted for this specific problem.Previous problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42408-divisible-by-6">divisible by 6</a>. Next problem: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/42410-divisible-by-8">divisible by 8</a>.

Pursuant to the <http://www.mathworks.com/matlabcentral/cody/problems/42404-divisible-by-2 first problem> in this series, this one involves checking for divisibility by 7.

Write a function to determine if a number is divisible by 7. This can be done by a variety of methods. Some are:

# Multiply each digit in the candidate number (from right to left) by the digit in the corresponding position in this pattern: 1, 3, 2, -1, -3, -2 (1 applies to the ones digit, 3 to the tens digit, etc.). This pattern should be repeated beyond the hundred-thousands digit. The resulting sum will be a smaller number. This method can be applied recursively to the absolute values of the resulting sum until a single digit results. Then, check that number for divisibility by seven.
# The previous method can also be used applying a slightly different pattern: 1, 3, 2, 6, 4, 5 (1 applies to the ones digit again, etc.). The absolute value of the resulting sum is not necessary as none of the factors are negative.
# Multiply the last (ones) digit by two and subtract the result from the remaining number. Apply recursively, as noted in methods above.
# Similar to the previous method, multiply the last digit by five and add to the remaining number. Apply recursively, as noted in methods above.
# Double the last digit and subtract it from the remaining number (original number except for the ones digit). Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.
# Similar to the previous method, multiply the ones digit by five and add it to the remaining number. Apply this recursively until a single digit results. If that number is divisible by seven, then so is the original number.
# Along similar lines, take the last three digits of the number and subtract that number from the remaining number. Once you reach a number less than 1000, another method can be applied to further reduce the number to check for divisibility by seven.
# Etc. (there are others)

The restriction for multiplication has been lifted for this specific problem.

Previous problem: <http://www.mathworks.com/matlabcentral/cody/problems/42408-divisible-by-6 divisible by 6>. Next problem: <http://www.mathworks.com/matlabcentral/cody/problems/42410-divisible-by-8 divisible by 8>.

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Problem 42409. Divisible by 7

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