document.write( "Question 491972: There is a positive two-digit integer that is divisible by the sum of its digits AND that has exactly 5 factors. What is the sum of its factors? \n" ); document.write( "
Algebra.Com's Answer #334864 by Edwin McCravy(20060)\"\" \"About 
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document.write( "For any integer the numbers\r\n" );
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document.write( "A. one of its factors \r\n" );
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document.write( "and \r\n" );
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document.write( "B. \"%28that_integer%29%2F%28that_factor%29\" \r\n" );
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document.write( "are two different integers except when the integer is a\r\n" );
document.write( "perfect square and that factor is its square root.\r\n" );
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document.write( "So only perfect squares have an odd number of factors, since\r\n" );
document.write( "its square root and \"%28that_perfect_square%29%2F%28its_square_root%29\" are not two different\r\n" );
document.write( "factors, but only one factor, since those are the same number. \r\n" );
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document.write( "So it has to be a perfect square to have 5 factors.\r\n" );
document.write( "So it has to be one of these:\r\n" );
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document.write( "16, 25, 36, 49, 64, or 81\r\n" );
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document.write( "16 is not divisible by 1+6, which is 7\r\n" );
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document.write( "25 is not divisible by 2+5, which is 7\r\n" );
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document.write( "36 IS divisible by 3+6, which is 9.  However 36 has \r\n" );
document.write( "       9 factors 1,2,3,4,6,9,12,18, and 36, and that's too many.\r\n" );
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document.write( "64 is not divisible by 6+4, which is 10.\r\n" );
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document.write( "81 is divisible by 8+1, which is 9.  It's factors are 1,3,9,27, and 81.\r\n" );
document.write( "       And that's 5, so the number is 81.\r\n" );
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document.write( "Answer: The sum of the factors is 1+3+9+27+81 = 121\r\n" );
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document.write( "Edwin
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