Re: count zeros in a number

• To: mathgroup at smc.vnet.net
• Subject: [mg121803] Re: count zeros in a number
• From: Andrzej Kozlowski <akozlowski at gmail.com>
• Date: Mon, 3 Oct 2011 04:21:43 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110020636.CAA28027@smc.vnet.net>

```On 2 Oct 2011, at 08:36, dimitris wrote:

> Hello.
>
> Consider e.g. the number 24^24*55^55.
> This number ends with exactly 55 zeros as the following demonstrate
>
> In[201]:= Mod[24^24*55^55, 10^55]
> Mod[24^24*55^55, 10^56]
>
> Out[201]= 0
> Out[202]= 20000000000000000000000000000000000000000000000000000000
>
>
> What I want now is a way to count the zeros that a number ends without
> knowing in advance this number of zeros like in the above example.
>
> Dimitris
>

Probably the most obvious way is to let Mathematica multiply out the numbers and count the trailing zeros, eg.

Length[Last[Split[IntegerDigits[24^24*55^55]]]]

55

An alternative approach is to just count the exponents of 5 and 2 and take the smaller one:

Min[
Cases[FactorInteger[24^24*55^55], {2, x_} | {5, y_} :> {x, y}]]

55

Andrzej Kozlowski

```

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