Math Is Fun Forum

Ritz

Guest

Trailing zeroes in factorials

How do we find number of trailing zeroes in factorials?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: Trailing zeroes in factorials

hi Ritz

Welcome to the forum.

A new zero will be added when a new factor of 2 and 5 occurs, as 2x5 = 10.  As every other number has 2 as a factor there won't be a shortage of them, so it's down to when does a factor of 5 occur.  The first time is 5! = 24 x 5 = 120.  Then 10! (=3628800) will add another and so on.

Writing a factorial as a product of primes should make this clear:

10! = (5x2) x (3x3) x (2x2x2) x 7 x (3x2) x 5 x (2x2) x 3 x 2 x 1

Bob

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Children are not defined by school ...........The Fonz
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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trailing zeroes in factorials

Hi;

There is a popular formula, say you wanted to know the number of trailing zeroes in 10000!. You just keep dividing by powers of 5.

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