document.write( "Question 119101: This is one of those GRE questions\r
\n" ); document.write( "\n" ); document.write( "column A
\n" ); document.write( "The greatest prime factor of 3^5\r
\n" ); document.write( "\n" ); document.write( "column B
\n" ); document.write( "The greatest prime factor of 5^3\r
\n" ); document.write( "\n" ); document.write( "a)column a is greater
\n" ); document.write( "b)column b is greater
\n" ); document.write( "c)the quantities are equal
\n" ); document.write( "d)relationship cannot be determined\r
\n" ); document.write( "\n" ); document.write( "I have always had trouble doing problems with prime numbers. Is there an easy way to do it because I can only do it by guess and check. Thanks for your help \n" ); document.write( "

Algebra.Com's Answer #87204 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is one of those GRE questions \r
\n" ); document.write( "\n" ); document.write( "column A
\n" ); document.write( "The greatest prime factor of 3^5
\n" ); document.write( "column B
\n" ); document.write( "The greatest prime factor of 5^3
\n" ); document.write( "a)column a is greater
\n" ); document.write( "b)column b is greater
\n" ); document.write( "c)the quantities are equal
\n" ); document.write( "d)relationship cannot be determined
\n" ); document.write( "

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document.write( "A prime number is a positive integer greater than 1 \r\n" );
document.write( "which is not divisible by any number except itself\r\n" );
document.write( "and 1.\r\n" );
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document.write( "All the factors are 3, 3^2, 3^3, 3^4 and 3^5.   \r\n" );
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document.write( "3 is not divisible by any positive integer besides itself, 3, and \r\n" );
document.write( "1 and it is greater than 1, so it IS a prime factor of 3^5\r\n" );
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document.write( "3^2, which is 9, is divisible by the positive integer 3, and 3 is\r\n" );
document.write( "a positive integer other than 9. So it is NOT a prime factor of 3^5.\r\n" );
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document.write( "3^3, which is 27, is divisible by the positive integer 3, and 3 is\r\n" );
document.write( "a positive integer other than 27. So it is NOT a prime factor of 3^5.\r\n" );
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document.write( "3^4, which is 81, is divisible by the positive integer 3, and 3 is\r\n" );
document.write( "a positive integer other than 81. So it is NOT a prime factor of 3^5.\r\n" );
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document.write( "3^5, which is 243, is divisible by the positive integer 3, and 3 is\r\n" );
document.write( "a positive integer other than 243. So it is NOT a prime factor of 3^5.\r\n" );
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document.write( "Therefore the largest prime factor of 3^5 is 3.  [Can you see, from the\r\n" );
document.write( "pattern above that 3 is the largest prime factor of even\r\n" );
document.write( "3*1000000000 ?]\r\n" );
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document.write( "Can you also see, by the same reasoning, that the largest prime factor \r\n" );
document.write( "of 5^3 is 5? \r\n" );
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document.write( "answer (a) says 3 is greater than 5.  We know that's incorrect.\r\n" );
document.write( "answer (b) says 5 is greater than 3.  We know that's correct.\r\n" );
document.write( "answer (c) says 3 is equal to 5.  We know that's incorrect.\r\n" );
document.write( "answer (d) say which is larger cannot be determined. We know that's\r\n" );
document.write( "  incorrect because we can determine that 5 is greater than 3.\r\n" );
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document.write( "The only correct answer is (b) \r\n" );
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document.write( "Edwin

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