11 Aug, 2010

Find the number of zero's in 'Factorial of a number' N factorial

For n as the number,

round(n/5) + round(n/25) + round(n/125)+.......+round(n/5^n)

etc till the reminder is 0.

Explain how?

A zero is formed when a 5 and 2 get multiplied, therefore finding the number of 5's would be enough to find the number of 10's since 5's would be less in number than 2. Lets take an example 30! = 1 x 2 .. x 5 x... x 10 .. x 15 ..x. 25 ... 30 It has 7 fives. Number of 5's can be found out by plainly dividing the number by 5 which gives you 6, But there is an extra 5 in the 25 since 25 = 5*5, which can be got again by dividing the number 5. So continuing so on, we get the above formulae..
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Comments (1) Post a comment

  • True - except...

    This is only true for "trailing" zeroes.
    13! = 6227020800 = 4 zeroes.
    But 14! = 87178291200 = 2 zeroes.

    I think your formula breaks down...

    By Anonymous on 22 Aug, 2011 Reply
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