<PRE><B>Question 550226</B>
51&lt;P&gt;
201! - 200! = 201*200! - 200! = 200*200!&lt;P&gt;
To find the number of trailing zeros in any n! determine the number of times it is divisible by all smaller powers of 5.  &lt;P&gt;
The reason it works is that zeros happen whenever 10 is a factor, and 5 and 2 are factors of 10.  Find the number of 5&#39;s that factor into the n! n, also the number of 5x5&#39;s and 5x5x5&#39;s etc.&lt;P&gt;
Ignore remainders&lt;P&gt;
200/5 = 40 + 200/25=8 + 200/125=1 = 49.&lt;P&gt;
But this n! is multiplied by another number.  Each of the zeros at the end of 200 will create a trailing 0.  So it&#39;s 49+2 = 51.&lt;P&gt;

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