13.335. If a two-digit number is divided by the product of its digits, the quotient is 3 and the remainder is 8. If the number, formed by the same digits but in reverse order, is divided by the product of the digits, the quotient is 2 and the remainder is 5. Find this number.
## Solution.

Let $10 x+y$ be the desired number. According to the condition, we have the system

$$
\left\{\begin{array}{l}
10 x+y=3 x y+8 \\
10 y+x=2 x y+5
\end{array}\right.
$$

Answer: 53.