document.write( "Question 1189427: What is the greatest whole number that MUST be a factor of the sum of any six consecutive positive odd numbers?
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Algebra.Com's Answer #820783 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "ANSWER.  The sum must be multiple of 12.\r\n" );
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document.write( "Proof\r\n" );
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document.write( "Let n be the \"central\" number in the sequence of 6 consecutive odd numbers\r\n" );
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document.write( "    (n-5), (n-3), (n-1), (n+1), (n+3), (n+5).\r\n" );
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document.write( "Then the sum is 6n, and since n is an even number n = 2m, 6n = 12m is a multiple of 12.\r\n" );
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document.write( "Since m can be any prime number, it shows that there is no other common divisor of the sums\r\n" );
document.write( "of this kind.\r\n" );
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