document.write( "Question 1186270: A six-digit number is formed by repeating a three-digit number as in 639639. Find the sum of the prime factors all such numbers have in common. \n" ); document.write( "

Algebra.Com's Answer #817153 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "A six-digit number is formed by repeating a three-digit number as in 639639.
\n" ); document.write( "Find the sum of the prime factors all such numbers have in common.
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document.write( "All these six-digit numbers, described in the post, are of the form\r\n" );
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document.write( "      N = 1000n + n = 1001n,\r\n" );
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document.write( "where n is a/(any) three digit number.\r\n" );
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document.write( "Therefore, all such 6-digit numbers have common factor  1001.\r\n" );
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document.write( "Its prime decomposition is 1001 = 7*11*13.\r\n" );
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document.write( "Its positive prime factors are  7, 11, 13.\r\n" );
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document.write( "The sum of these factors is 7 + 11 + 13 = 31.\r\n" );
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document.write( "ANSWER.  31.\r\n" );
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