Composite numbers which divide the concatenation of their prime factors in chaos order

Question

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 ?

Answer 1

There are $13$ Ken's numbers below $1000$. Five more are:

• $474\mid 3792$
• $548\mid 21372$
• $576\mid 22223232$
• $612\mid 233172$
• $636\mid 23532$

Answer 2

Note that $28749$ is a Ken's number which also happens to be divide the concatenation of its prime factors in the neat ascending order:

• $28749$ = $37$.$3$.$7$.$37$
• $28749$ = $3$.$7$.$37$.$37$
• $28749$ = $37$.$37$.$3$.$7$
• And $28749\mid 373737$

$28749$ is not exactly dividing in three ways, since $37$.$3$.$7$.$37$ and $37$.$37$.$3$.$7$ and $3$.$7$.$37$.$37$ concatenated to the same number $373737$.