It's Time to Digit-Spread!

$\begin{array}{ccccc} & & & A & B\\ \times & & & & C\\ \hline & & A & 0 & B\\ \hline \end{array}$ Each of the letters contains distinct single-digit integer. What must be true about the divisibility of $\overline{A0B}$ , where the center digit is the number $0$ ?

Bonus: It is possible that $\overline{AB} \times \overline{CD} = \overline{A00B}$ . Can we multiply $\overline{AB}$ by a number with more distinct digits to obtain the product of the form $\left(A\times 10^n + B\right)$ , where $n$ is some positive integer?