document.write( "Question 162241: The product of two prime numbers is 221. Their GCF is 1 and their LCM is 221. What are the two prime numbers? \n" ); document.write( "

Algebra.Com's Answer #119562 by Edwin McCravy(20055) $\"\"$ $\"About$

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The product of two prime numbers is 221. Their GCF is 1 and their LCM is 221. What are the two prime numbers?
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document.write( "The prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,...\r\n" );
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document.write( "Get a calculator and start dividing 221 by these prime\r\n" );
document.write( "numbers until you find one that doesn't have a decimal:\r\n" );
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document.write( "221÷2=110.5         That has a decimal, so we keep going:\r\n" );
document.write( "221÷3=73.66666667   That has a decimal, so we keep going:\r\n" );
document.write( "221÷5=44.2          That has a decimal, so we keep going:\r\n" );
document.write( "221÷7=31.57142857   That has a decimal, so we keep going:\r\n" );
document.write( "221÷11=20.09090909  That has a decimal, so we keep going:\r\n" );
document.write( "221÷13=17           Aha!  No decimal! And the quotient, 17,\r\n" );
document.write( "is a prime number itself!\r\n" );
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document.write( "So the answer is:  The two prime numbers you are looking\r\n" );
document.write( "for are 13 and 17.  \r\n" );
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document.write( "Checking: Multiply them 13x17 = 221.  So their product is\r\n" );
document.write( "221.  The only factors of 13 are 13 and 1.  The only factors\r\n" );
document.write( "of 17 and 1.  So they have only one common factor, namely 1.\r\n" );
document.write( "And since it is the ONLY common factor is has to be the \r\n" );
document.write( "GREATEST common factor.\r\n" );
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document.write( "So 13 and 17 are the two prime numbers you were looking for.\r\n" );
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document.write( "Edwin

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