SOLUTION: Find the number of trailing zeroes in the product of the first n factorials

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Question 1111875: Find the number of trailing zeroes in the product of the first n factorials
Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
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Calculate the highest degree of 5 in the product: it will give you the number of zeroes.


The highest degree of 5 is equal to


[n/5] + [n/5^2] + [n/5^3] + . . . + [n/5^m],


where [x] means the "integer part" of the number x  (do not ask me what is it - you must know it); 
 
the index "m" is the highest degree the number  5%5Em  still divides n.