document.write( "Question 990558: The number of ways in which the number 27720 can be split into two factors which are coprimes is \n" ); document.write( "
Algebra.Com's Answer #610795 by Edwin McCravy(20056)\"\" \"About 
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document.write( "27720 = 2³*3²*5*7*11\r\n" );
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document.write( "There are 5 prime factors. Since the two factors of 27720 must be coprime, if we\r\n" );
document.write( "choose a 2 for one factor to contain, we must choose 2³ for that factor to\r\n" );
document.write( "contain.  Similarly if we choose a 3 for one factor we must choose 3² for that\r\n" );
document.write( "factor to contain.  So it depends on how many prime factors, not how many times\r\n" );
document.write( "the prime factors are contained in 22720. \r\n" );
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document.write( "Case 1:\r\n" );
document.write( "Number of ways we can choose 1 prime factor for the first and 4 prime factors\r\n" );
document.write( "for the second.\r\n" );
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document.write( "That's 5C1 = 5 ways\r\n" );
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document.write( "1. first factor = 2³, second factor = 3²*5*7*11\r\n" );
document.write( "2. first factor = 3², second factor = 2³*5*7*11\r\n" );
document.write( "3. first factor = 5, second factor = 2³*3²*7*11\r\n" );
document.write( "4. first factor = 7, second factor = 2³*3²*5*11\r\n" );
document.write( "5. first factor = 11, second factor = 2³*3²*5*7\r\n" );
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document.write( "Case 2:\r\n" );
document.write( "Number of ways we can choose 2 prime factors for the first and 3 prime factors\r\n" );
document.write( "for the second.\r\n" );
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document.write( "That's 5C2 = 10 ways\r\n" );
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document.write( "1. first factor = 2³*3², second factor = 5*7*11\r\n" );
document.write( "2. first factor = 2³*5, second factor = 3²*7*11\r\n" );
document.write( "3. first factor = 2³*7, second factor = 3²*5*11\r\n" );
document.write( "4. first factor = 2³*11, second factor = 3²*5*7\r\n" );
document.write( "5. first factor = 3²*5, second factor = 2³*7*11\r\n" );
document.write( "6. first factor = 3²*7, second factor = 2³*5*11\r\n" );
document.write( "7. first factor = 3²*11, second factor = 2³*5*7\r\n" );
document.write( "8. first factor = 5*7, second factor = 2³*3²*11\r\n" );
document.write( "9. first factor = 5*11, second factor = 2³*3²*7\r\n" );
document.write( "10. first factor = 7*11, second factor = 2³*3²*5\r\n" );
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document.write( "Answer 5C1 + 5C2 = 5 + 10 = 15 ways.\r\n" );
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document.write( "Edwin
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