document.write( "Question 1115766: The notation n! = n•(n-1)•(n–2)• • • • • •3•2•1. For example, 5! = 5•4•3•2•1 = 120. How many zeroes occur at the end of the expanded numeral for 100!? \n" ); document.write( "

Algebra.Com's Answer #730596 by MathLover1(20850) $\"\"$ $\"About$

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The number of trailing zeros in the decimal representation of $\"n%21\"$ , the factorial of a non-negative integer $\"n\"$ , can be determined with this formula:\r
\n" ); document.write( "\n" ); document.write( " $\"n%2F5%2Bn%2F5%5E2%2Bn%2F5%5E3\"$ +...+ $\"n%2F5%5Ek\"$ where $\"k\"$ must be chosen such that $\"5%5E%28k%2B1%29%3En\"$ \r
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\n" ); document.write( "\n" ); document.write( "so, $\"100%21\"$ has $\"100%2F5%2B100%2F5%5E2=100%2F5%2B100%2F25=20%2B4=24\"$ trailing zeros \n" ); document.write( "

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