document.write( "Question 696511: Find the sum of all 4 digit natural numbers of the form 4AB8 which are divisible by 2,3,4,6,8, and 9 \n" ); document.write( "
Algebra.Com's Answer #429101 by Edwin McCravy(20055)\"\" \"About 
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document.write( "To be divisible by 2,3,4,6,8, and 9\r\n" );
document.write( "we list all the like factors in\r\n" );
document.write( "columns to get the least common\r\n" );
document.write( "multiple of all those: \r\n" );
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document.write( "2=     2\r\n" );
document.write( "3=           3\r\n" );
document.write( "4=     2·2 \r\n" );
document.write( "6=     2    ·3 \r\n" );
document.write( "8=     2·2·2 \r\n" );
document.write( "9=           3·3\r\n" );
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document.write( "       2·2·2·3·3 = 72 \r\n" );
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document.write( "So we find all the multiples of 72\r\n" );
document.write( "that are 4-digits, that begin with a\r\n" );
document.write( "4 and end with an 8.\r\n" );
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document.write( "The smallest feasible number is\r\n" );
document.write( "4008, which divided by 72 gives 55.66,\r\n" );
document.write( "a decimal, not a whole number.\r\n" );
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document.write( "The largest feasible number is\r\n" );
document.write( "4998, which divided by 72 gives 69.42,\r\n" );
document.write( "also a decimal, not a whole number.\r\n" );
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document.write( "Of course neither of those qualify,\r\n" );
document.write( "but they tell us the bounds to look\r\n" );
document.write( "for numbers to multiply by 72. Since \r\n" );
document.write( "72 ends in 2, to get a number\r\n" );
document.write( "ending in 8, we know that a number\r\n" );
document.write( "ending in 4 will give an answer\r\n" );
document.write( "ending in 8, since 2·4 = 8.  Also we\r\n" );
document.write( "know that a number ending in 9 \r\n" );
document.write( "multiplied by 72 will give an answer\r\n" );
document.write( "ending in 8 since 2·9 = 18.  \r\n" );
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document.write( "The only two digit numbers in that\r\n" );
document.write( "range which end in 4 or 9 are\r\n" );
document.write( "59, 64, and 69.  Multiplying them by\r\n" );
document.write( "72 gives the answers\r\n" );
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document.write( "72·59 = 4248\r\n" );
document.write( "72·64 = 4608\r\n" );
document.write( "72·69 = 4968\r\n" );
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document.write( "Add them up and get 13824\r\n" );
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document.write( "Edwin
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