document.write( "Question 118763: This has us stumped.Its called Ms.DeYoungs BUNGEE
\n" ); document.write( "All numbers must meet the following requirements:
\n" ); document.write( "1. must be even numbers
\n" ); document.write( "2.must be a multiple of 12
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\n" ); document.write( "4.must possess at least 1000 factors
\n" ); document.write( "5.If a standard numeral, must have exactly four terminal zeroes showing\r
\n" ); document.write( "\n" ); document.write( "A: 2 8th power X 3 4th power X 5 forth power X 17 4th power
\n" ); document.write( "B: 2 2nd power X 7 eigth power X 11 forth power X 17 sixth power X 23 fifth power
\n" ); document.write( "C: 2 forth power X 7 eigth power X 13 forth power X 19 2nd power
\n" ); document.write( "D: 2 forth power X 3 eigth power X 5 forth power X 13 2nd power X 97
\n" ); document.write( "E: 3 fifth power X 5 seveth power X 11 forth power X 13 2nd power X 23
\n" ); document.write( "F: 2 sixth power X 3 2nd power X 5 forth power X 7 forth power X 23 sixth power\r
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Algebra.Com's Answer #86914 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "This has us stumped.Its called Ms.DeYoungs BUNGEE\r\n" );
document.write( "All numbers must meet the following requirements:\r\n" );
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document.write( "1. must be an even number\r\n" );
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document.write( "So it must have factor 2.\r\n" );
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document.write( "2. must be a multiple of 12\r\n" );
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document.write( "So it must contain the factor 12. That means that it\r\n" );
document.write( "must have 2231 as a factor.\r\n" );
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document.write( "3.must be a perfect square\r\n" );
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document.write( "This means that it must have another 3 as a factor. So far\r\n" );
document.write( "it must have 2232 as a factor.\r\n" );
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document.write( "4.must possess at least 1000 factors\r\n" );
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document.write( "We will use this number-of-factors rule (theorem):\r\n" );
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document.write( "If a positive integer is factored into its prime power factors,\r\n" );
document.write( "then the total number of factors is found by adding one to all\r\n" );
document.write( "the exponents and multiplying those results together.\r\n" );
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document.write( "So it must obey the above rule.\r\n" );
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document.write( "5.If written as a standard numeral, must have exactly four \r\n" );
document.write( "terminal zeroes showing\r\n" );
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document.write( "This means it is a multiple of 10000.  10000 = \"10%5E4\" =\r\n" );
document.write( "2454.  All the properties except property 4\r\n" );
document.write( "are satisfied if 243254 is a factor.\r\n" );
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document.write( "A: 2 8th power X 3 4th power X 5 forth power X 17 4th power\r\n" );
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document.write( "This has 243254 as a factor so we \r\n" );
document.write( "only need investigate to see if it meets the above \r\n" );
document.write( "number-of-factors rule in property 4. \r\n" );
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document.write( "The exponents are 8,4,4,4. Add 1 to each one: 9,5,5,5.  Multiply\r\n" );
document.write( "9x5x5x5 = 1125.  So it has 1125 factors.  This is more than 1000,\r\n" );
document.write( "So it meets all the properties. \r\n" );
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document.write( "B: 2 2nd power X 7 eigth power X 11 forth power X 17 sixth power\r\n" );
document.write( "  X 23 fifth power\r\n" );
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document.write( "243254 is not a factor of it so it does not have all the properties.  It \r\n" );
document.write( "needs to be multiplied by 223254 in order to have 243254 as a factor. \r\n" );
document.write( "Its exponents are large enough for it to have 1000 factors, \r\n" );
document.write( "so it does have property 4, since its exponents are 2,8,4,6,5; \r\n" );
document.write( "adding 1 to each gives 3,9,5,7,6 and 3x9x5x7x6 = 5670. \r\n" );
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document.write( "C: 2 fourth power X 7 eigth power X 13 fourth power X 19 2nd power\r\n" );
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document.write( "243254 is not a factor of it\r\n" );
document.write( "so it does not have all the properties.  It needs to be multiplied \r\n" );
document.write( "by 3254 in order to have 243254 as a factor. Its\r\n" );
document.write( "exponents are not large enough for it to have 1000 factors, so it \r\n" );
document.write( "does not have property 4, since its exponents are 4,8,4,2; adding \r\n" );
document.write( "1 to each gives 5,9,5,3 and 5x9x5x3 = 675.  If we multiplied it by \r\n" );
document.write( "3254 then it would have at \r\n" );
document.write( "least 1000 factors.\r\n" );
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document.write( "D: 2 fourth power X 3 eigth power X 5 fourth power X 13 2nd power X 97\r\n" );
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document.write( "This has 243254 as a factor so we only need investigate to see \r\n" );
document.write( "if it meets the above number-of-factors rule in property 4. \r\n" );
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document.write( "The exponents are 4,8,4,2,1. Add 1 to each one: 5,9,5,3,2.  Multiplying\r\n" );
document.write( "5x9x5x3x2 = 1350.  So it has 1350 factors.  This is more than 1000,\r\n" );
document.write( "So it meets all the properties.\r\n" );
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document.write( "E: 3 fifth power X 5 seventh power X 11 fourth power X 13 2nd power X 23\r\n" );
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document.write( "243254 is not a factor of it so it does not have all the properties.  \r\n" );
document.write( "It needs to be multiplied by 24 in order to have 243254 as a factor. Its exponents\r\n" );
document.write( "are large enough for it to have 1000 factors, so it does have property 4,\r\n" );
document.write( "since its exponents are 5,7,4,2,1; adding 1 to each gives 6,8,5,3,2 and \r\n" );
document.write( "6x8x5x3x2 = 1440 \r\n" );
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document.write( "F: 2 sixth power X 3 2nd power X 5 forth power X 7 forth power X 23 \r\n" );
document.write( "sixth power\r\n" );
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document.write( "This has 253254 as a factor so we only need\r\n" );
document.write( "investigate to see if it meets the above number-of-factors rule in property 4. \r\n" );
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document.write( "The exponents are 6,2,4,4,6. Add 1 to each one: 7,3,5,5,7.  Multiply\r\n" );
document.write( "7x3x5x5x7 = 3675.  So it has 3675 factors.  This is more than 1000,\r\n" );
document.write( "So it meets all the properties.\r\n" );
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document.write( "Edwin
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