13.157. Find a two-digit number such that if it is divided by the product of the digits it is composed of, the quotient is $16 / 3$, and if 9 is subtracted from it, the difference will also be a two-digit number that differs from the desired number only in the order of the digits.
## Solution.

Let $10 x+y$ be the desired two-digit number. Then

$$
\left\{\begin{array}{l}
\frac{10 x+y}{x y}=\frac{16}{3}, \\
10 x+y-9=10 y+x,
\end{array} \text { from which } x=3, y=2 . \text { The desired number is } 32 .\right.
$$

Answer: 32.