Find the maximum possible number

Question

I've tried to rewrite each number descriptively and I turn out to:

But I do think I'm missing something

Answer 1

Hint. Let $x=\overline{bcd}$ then $$1000a+x=(a+1)x+100a+56\implies x=900-\frac{56}{a}\in\mathbb{N}.$$ Hence the digit $a$ divides $56=2^3\cdot 7$. Since here we are looking for the maximum, we should try first with the case $a=8$.