document.write( "Question 960568: How many zeroes at the end of 25!pls help with explanation.thanks in advance \n" ); document.write( "

Algebra.Com's Answer #587327 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "A positive integer has exactly as many 0's at the end as the largest \r\n" );
document.write( "exponent of 10 which is a factor of the positive integer.\r\n" );
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document.write( "Since 10 = 2*5, we can make the following statement:\r\n" );
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document.write( "Suppose the prime factorization of a positive integer has \r\n" );
document.write( "n factors of 5 and m factors of 2.\r\n" );
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document.write( "Then if m > n, then the positive integer has exactly n 0's at the end\r\n" );
document.write( "if m < n, then the positive integer has exactly m 0's at the end.\r\n" );
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document.write( "The prime factorization of 25! contains more factors of 2 than it has\r\n" );
document.write( "factors of 5, so we only need to know the number of factors of 5.  \r\n" );
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document.write( "The prime factorization of  gets 1 factor of 5\r\n" );
document.write( "from its factors of 5,10,15, and 20, and 2 factors of 5 from its factor\r\n" );
document.write( "of 25.  So the prime factorization of 25! has 6 factors of 5, so it has\r\n" );
document.write( "6 zeros at the end.\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "25! = 15511210043330985984000000   \r\n" );
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document.write( "Edwin

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