document.write( "Question 80803: what are the factors of the number 2400? and how many are there in total? \n" ); document.write( "
Algebra.Com's Answer #57987 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
what are the factors of the number 2400? and how many are there in total?\r
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document.write( "Break 2400 down into prime factors with a factor tree:\r\n" );
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document.write( "2400 = 2·2·2·2·2·3·5·5\r\n" );
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document.write( "It's easy to answer the last question.  There are only\r\n" );
document.write( "3 prime factors of 2400. These are 2,3,and 5.  So\r\n" );
document.write( "every factor is of the form\r\n" );
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document.write( "2P3Q5R\r\n" );
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document.write( "where P can take on values 0,1,2,3,4,5, that's 6 factors\r\n" );
document.write( "      Q can take on values 0,1, that's 2 factors\r\n" );
document.write( "      R can take on values 0,1,2, that's 3 factors\r\n" );
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document.write( "So that's a total of 6·2·3 = 36 factors.\r\n" );
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document.write( "But to get all those 36 factors is a lot of busy work:\r\n" );
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document.write( "We make all the combinations of those factors:\r\n" );
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document.write( "Combinations of one factor:\r\n" );
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document.write( "1, 2, 3, and 5\r\n" );
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document.write( "This accounts for 4 factors\r\n" );
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document.write( "Combinations of two factors:\r\n" );
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document.write( "2·2, 2·3, 2·5, 3·5. 5·5 or\r\n" );
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document.write( "This accounts for 5 factors\r\n" );
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document.write( "Combination of three factors:\r\n" );
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document.write( "2·2·2, 2·2·3, 2·2·5, 2·3·5, 2·5·5, 3·5·5\r\n" );
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document.write( "This accounts for 6 factors\r\n" );
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document.write( "Combinations of four factors:\r\n" );
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document.write( "2·2·2·2, 2·2·2·3, 2·2·2·5, 2·2·3·5, 2·2·5·5, 2·3·5·5 \r\n" );
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document.write( "This accounts for 6 factors\r\n" );
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document.write( "-----------------------------\r\n" );
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document.write( "Combinations of five factors:\r\n" );
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document.write( "2·2·2·2·2, 2·2·2·2·3, 2·2·2·2·5, 2·2·2·3·3, 2·2·2·3·5, 2·2·2·5·5, 2·2·3·5·5\r\n" );
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document.write( "This accounts for 7 factors\r\n" );
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document.write( "Combinations of six factors:\r\n" );
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document.write( "2·2·2·2·2·3, 2·2·2·2·2·5, 2·2·2·2·3·5, 2·2·2·3·5·5\r\n" );
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document.write( "This accounts for 4 factors\r\n" );
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document.write( "Combinations of seven factors:\r\n" );
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document.write( "2·2·2·2·2·3·5, 2·2·2·2·2·5·5, 2·2·2·2·3·5·5\r\n" );
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document.write( "This accounts for 3 factors\r\n" );
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document.write( "Combinations of eight factors:\r\n" );
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document.write( "2·2·2·2·2·3·5·5\r\n" );
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document.write( "This accounts for 1 factor.\r\n" );
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document.write( "That's  4 + 5 + 6 + 6 + 7 + 4 + 3 + 1 = 36 factors, so we have them\r\n" );
document.write( "all. These are, in order:\r\n" );
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document.write( "1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50,\r\n" );
document.write( "60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800,\r\n" );
document.write( "1200, 2400\r\n" );
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document.write( "Edwin
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