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Re: Trailing zeros of 100!

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From Peter Otten <__peter__@web.de>
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Subject Re: Trailing zeros of 100!
Date Sat, 02 Jan 2016 18:18:05 +0100
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Robin Koch wrote:

> Am 02.01.2016 um 12:49 schrieb katye2007@gmail.com:
> 
>> I'm trying to write a python program to find how many trailing zeros
>> are in 100! (factorial of 100). I used factorial from the math
>> module, but my efforts to continue failed. Please help.
> 
> Using not Python, but math:
> 
> Every "0" at the end of 100! represents a multiplication by the factor
> 10 or the factors 2 and 5.
> 
> There are 20 numbers with at least one factor 5.
> There are  4 numbers with at least two factors 5 (=25).
> There are no numbers with three factors 5 (=125).
> 
> There are 50 numbers with at least one factor 2.
> 
> So 100! contains 24 factors 5 and even more factors 2.
> So 100! contains 24 facotrs 10 and therefore has 24 trailing zeros.

Spelt in Python:

>>> def trailing_zeros_fact(n):
...     total = 0
...     while n:
...         n //= 5
...         total += n
...     return total
... 
>>> trailing_zeros_fact(100)
24
>>> trailing_zeros_fact(math.factorial(100))
23331553860986038170424809714066675122678992066095405367148240973804399998307478902235365994039129571563424480206805939562796302729215999999999999999999999901

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Trailing zeros of 100! katye2007@gmail.com - 2016-01-02 03:49 -0800
  Re: Trailing zeros of 100! David <bouncingcats@gmail.com> - 2016-01-02 23:19 +1100
  Re: Trailing zeros of 100! katye2007@gmail.com - 2016-01-02 04:34 -0800
  Re: Trailing zeros of 100! Vlastimil Brom <vlastimil.brom@gmail.com> - 2016-01-02 13:44 +0100
  Re: Trailing zeros of 100! "yehudak ." <katye2007@gmail.com> - 2016-01-02 15:14 +0200
    Re: Trailing zeros of 100! Robin Koch <robin.koch@t-online.de> - 2016-01-02 16:57 +0100
      Re: Trailing zeros of 100! Tony van der Hoff <tony@vanderhoff.org> - 2016-01-02 17:09 +0100
        Re: Trailing zeros of 100! Robin Koch <robin.koch@t-online.de> - 2016-01-02 17:56 +0100
          Re: Trailing zeros of 100! Bernardo Sulzbach <mafagafogigante@gmail.com> - 2016-01-02 15:24 -0200
          Re: Trailing zeros of 100! Chris Angelico <rosuav@gmail.com> - 2016-01-03 08:57 +1100
            Re: Trailing zeros of 100! Robin Koch <robin.koch@t-online.de> - 2016-01-03 01:02 +0100
              Re: Trailing zeros of 100! Ben Finney <ben+python@benfinney.id.au> - 2016-01-03 11:20 +1100
              Re: Trailing zeros of 100! srinivas devaki <mr.eightnoteight@gmail.com> - 2016-01-03 07:16 +0530
          Re: Trailing zeros of 100! Tony van der Hoff <tony@vanderhoff.org> - 2016-01-03 11:53 +0100
  Re: Trailing zeros of 100! Joel Goldstick <joel.goldstick@gmail.com> - 2016-01-02 09:57 -0500
  Re: Trailing zeros of 100! Vlastimil Brom <vlastimil.brom@gmail.com> - 2016-01-02 16:24 +0100
  Re: Trailing zeros of 100! Mark Lawrence <breamoreboy@yahoo.co.uk> - 2016-01-02 15:30 +0000
  Re: Trailing zeros of 100! Robin Koch <robin.koch@t-online.de> - 2016-01-02 16:54 +0100
    Re: Trailing zeros of 100! Peter Otten <__peter__@web.de> - 2016-01-02 18:18 +0100
  Re: Trailing zeros of 100! Tim Chase <python.list@tim.thechases.com> - 2016-01-02 10:33 -0600
  Re: Trailing zeros of 100! "yehudak ." <katye2007@gmail.com> - 2016-01-02 19:34 +0200
  Re: Trailing zeros of 100! Mark Lawrence <breamoreboy@yahoo.co.uk> - 2016-01-02 17:44 +0000
    Re: Trailing zeros of 100! Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-01-03 00:36 +0100
  Re: Trailing zeros of 100! Serhiy Storchaka <storchaka@gmail.com> - 2016-01-02 20:28 +0200
  Re: Trailing zeros of 100! Vlastimil Brom <vlastimil.brom@gmail.com> - 2016-01-02 19:29 +0100
  Re: Trailing zeros of 100! "yehudak ." <katye2007@gmail.com> - 2016-01-02 22:02 +0200
  Re: Trailing zeros of 100! "yehudak ." <katye2007@gmail.com> - 2016-01-02 22:09 +0200
  Re: Trailing zeros of 100! Mark Lawrence <breamoreboy@yahoo.co.uk> - 2016-01-02 21:25 +0000
  Re: Trailing zeros of 100! Mark Lawrence <breamoreboy@yahoo.co.uk> - 2016-01-02 21:26 +0000

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