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Talking BIG (Posted on 2017-11-10) Difficulty: 3 of 5
The number (10^(666))! where 666 is the beast number and "!" denotes a factorial is called Leviathan Number.

Given that this number has approximately 6.656×10^(668) decimal digits, evaluate the number of its trailing zeros.

No Solution Yet Submitted by Ady TZIDON    
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Good approximation, upper bound | Comment 1 of 3
The number of zeros is the number of factors of 5.  This is always smaller than 1/5 + 1/25 + 1/125 + 1/625 + ... = 1/4
and for large numbers, this estimate is quite good.  
For example
1000! has exactly 200+40+8+1=249 trailing zeros and 1/4 of 1000 is only greater by 1.

A good approximation then is 1/4 of 10^666 or 2.5*10^665




  Posted by Jer on 2017-11-10 08:34:45
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