Question 103
Let a four digit number $ABCD$ be called a *good number* if all its digits are distinct and nonzero, and the following are all integers: $\frac{CD}{AB}$, $\frac{C}{A}$, $\frac{D}{B}$. For example, the number $1284$ is good because all its digits are distinct, nonzero, and $\frac{84}{12} = 7$, $\frac{8}{1} = 8$, $\frac{4}{2} = 2$. Find all good numbers. It is not required to prove that there are no other good numbers.