document.write( "Question 163303: If a number is the square of a prime number, it has exactly 3 divisors. Give an example and explain. \n" ); document.write( "
Algebra.Com's Answer #120333 by Edwin McCravy(20055)\"\" \"About 
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document.write( "If a number is the square of a prime number, it has\r\n" );
document.write( "exactly 3 divisors. Give an example and explain.\r\n" );
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document.write( "Take the prime number 2.  Square it.  Get 4.  4\r\n" );
document.write( "has exactly three divisors. They are 1, 2 and 4,\r\n" );
document.write( "because all three of those but no others will divide\r\n" );
document.write( "evenly into 4.\r\n" );
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document.write( "Take the prime number 3.  Square it.  Get 9.  9 has \r\n" );
document.write( "exactly three divisors. They are 1, 3 and 9, because \r\n" );
document.write( "all three of those but no others will divide evenly into 9. \r\n" );
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document.write( "Take the prime number 5.  Square it.  Get 25.  25 has\r\n" );
document.write( "exactly three divisors. They are 1, 5 and 25, because all \r\n" );
document.write( "three of those but no others will divide evenly into 25.\r\n" );
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document.write( "Take the prime number 11.  Square it.  Get 121.  121 \r\n" );
document.write( "has exactly three divisors. They are 1, 11 and 121, because \r\n" );
document.write( "all three of those but no others will divide evenly into 11.\r\n" );
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document.write( "Now, to elaborate,  you might wonder if that would work if \r\n" );
document.write( "you started with a number other than a prime number.  The \r\n" );
document.write( "answer is no, but we need to demonstrate this:\r\n" );
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document.write( "Take the non-prime number 4.  Square it.  Get 16.  But 16 \r\n" );
document.write( "has FIVE divisors. They are 1,2,4,8,16. because all FIVE of \r\n" );
document.write( "those but no others will divide evenly into 16.\r\n" );
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document.write( "So it doesn't work for square of the non-prime 4.\r\n" );
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document.write( "Take the non-prime number 1.  Square it.  Get 1.  But 1 \r\n" );
document.write( "has only ONE divisor. That is 1 itself. because that is the \r\n" );
document.write( "only number that will divide evenly into 1.\r\n" );
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document.write( "So it doesn't work for the square of the non-prime 1 either.\r\n" );
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document.write( "Edwin
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