document.write( "Question 1039490: By which number should be multiplied 2352 to make prefect square by division method \n" ); document.write( "
Algebra.Com's Answer #654240 by Edwin McCravy(20055)\"\" \"About 
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document.write( "If p is a prime factor of a perfect square,\r\n" );
document.write( "then the maximum k for which pk is a factor,\r\n" );
document.write( "then k MUST be an even number.\r\n" );
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document.write( "We prime factor 2352 with a factor tree:\r\n" );
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document.write( "          2352\r\n" );
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document.write( "         2  1176 \r\n" );
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document.write( "           2   588\r\n" );
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document.write( "              2  294\r\n" );
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document.write( "                2  147\r\n" );
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document.write( "                 3   49\r\n" );
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document.write( "                   7    7\r\n" );
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document.write( "So 2352 = 24∙3∙72\r\n" );
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document.write( "The primes 2 and 7 already have even powers,\r\n" );
document.write( "so we must multiply by 3 so that the 3 will\r\n" );
document.write( "also have an even power.\r\n" );
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document.write( "So we must multiply by 3:\r\n" );
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document.write( "2352∙3 = 24∙32∙72\r\n" );
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document.write( "The answer is 3.  Then the perfect square will be\r\n" );
document.write( "7056, which is 24∙32∙72 \r\n" );
document.write( "and (22∙3∙7)2 = (4∙3∙7)2 = 842\r\n" );
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document.write( "Edwin
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