【Analysis】 $\overline{A B} \times \mathrm{k}=\overline{A C B} \quad(A \neq 0)$,
$$
\begin{aligned}
\mathrm{k} & =\frac{\overline{A C B}}{\overline{A B}}=\frac{100 A+10 C+B}{10 A+B}=\frac{100 A+10 B-9 B+10 C}{10 A+B} \\
& =\frac{10(10 A+B)+10 C-9 B}{10 A+B}=10+\frac{10 C-9 B}{10 A+B},
\end{aligned}
$$

To make $\mathrm{k}$ large, the numerator should be large, and the denominator should be small. When $\mathrm{A}$ takes the minimum value 1, $\mathrm{C}$ takes the maximum value 9, and $\mathrm{B}$ takes 0, the result is maximized. At this time, $\mathrm{k}=19$, reaching the maximum value, (for example: we can construct $10 \rightarrow 190 \quad 190 \div 10=19$ )
17. Insert a digit into a two-digit number to form a three-digit number. Some two-digit numbers, when a certain digit is inserted in the middle, become a three-digit number that is $k$ times the original two-digit number ($k$ is a positive integer). The maximum value of $k$ is ( ).