document.write( "Question 960569: What is the highest power of 15 in the expansion in 30!thanks in advance. \n" ); document.write( "
Algebra.Com's Answer #587081 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The factors that are multiplied in the expansion of 30! are\r\n" );
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document.write( "\"30%21+=+1%2A2%2A3%2A%22%22%2A%22%22%2A30\"\r\n" );
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document.write( "Every factor of 15 of 30! is a pair of factors of 5 and 3.\r\n" );
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document.write( "These 5 multiples of 5, which are 5,10,15,20, and 30 all contribute\r\n" );
document.write( "1 5 factor.  The factor 25 = 52 contributes 2 more factors of 5.  \r\n" );
document.write( "So there are 7 factors of 5 in the prime factorization of 30!.\r\n" );
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document.write( "There are more than 7 factors of 3 (In fact there are 14 factors of 3). \r\n" );
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document.write( "So 30! has 7 factors of 5. \r\n" );
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document.write( "So the 7 factors of 5 can be paired together with 7 of the factors of 3,\r\n" );
document.write( "making 7 factors of 15.\r\n" );
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document.write( "So the highest power of 15 that is a factor of 30! is 157, the seventh power.\r\n" );
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document.write( "Edwin

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