Since numbers divide the concatenation of their prime factors in neat ascending/descending order are have been listed at OEIS (See <https://oeis.org/A259047> and <https://oeis.org/248915> ). Here we are only talking about composite numbers which divide the concatenation of their prime factors in chaos order. Chaos order here means in any order but the neat ascending/descending order. For simplicity I will call such numbers a Ken's number. So a Ken's number is a composite number which divide the concatenation of its prime factors in chaos order. There are exactly $8$ Ken's numbers below $400$, and they are:

* $24=2\cdot 2\cdot 3\cdot 2$ and $24\mid2232$
* $44=2\cdot 11\cdot 2$ and $44\mid2112$
* $52=2\cdot 13\cdot 2$ and $52\mid2132$
* $105=7\cdot 3\cdot 5$ and $105\mid735$
* $114=3\cdot 19\cdot 2$ and $114\mid3192$
* $152=2\cdot 2\cdot 19\cdot 2$ and $152\mid22192$
* $176=2\cdot 2\cdot 2\cdot 11\cdot 2$ and $176\mid222112$
* $348=29\cdot 2\cdot 3\cdot 2$ and $348\mid29232$.

I have two questions:

> 
> 1. Can you find a larger example of ken's numbers?
> 2. Does there exist a Ken's number divides the concatenation of its prime
>  factors in three ways or more ?
> 
> 
>