# Numbers Factory

You are given a two or more digits number
**
N
**
.
For this mission, you should find the smallest positive number of
**
X
**
,
such that the product of its digits is equal to N.
If X does not exist, then return 0.

Let's examine the example. N = 20. We can factorize this number as 2*10, but 10 is not a digit. Also we can factorize it as 4*5 or 2*2*5. The smallest number for 2*2*5 is 225, for 4*5 -- 45. So we select 45.

**
Hints:
**
Remember prime numbers (numbers divisible by only one) and be careful with endless loops.

**
Input:
**
A number N as an integer.

**
Output:
**
The number X as an integer.

**
Example:
**

checkio(20) == 45 checkio(21) == 37 checkio(17) == 0 checkio(33) == 0

**
How it is used:
**
This task will teach you how to work with numbers in code.
You can factorize numbers and reconstruct them into new numbers.
Of course you can solve this problem with brute force,
but is that the best way?
Numbers are the foundation of mathematics and programming.

**
Precondition:
**

9 < N < 10
^{
5
}
.

CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

pip3 install checkio_client

Configure your tool

checkio --domain=py config --key=

Sync solutions into your local folder

checkio sync

(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)

checkio serv -d

Alternatevly, you can install Chrome extension or FF addon

checkio install-plugin

checkio install-plugin --ff

checkio install-plugin --chromium

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.