13.160. If a two-digit number is divided by the sum of its digits, the quotient is 4 and the remainder is 3. If this number is divided by the product of its digits, the quotient is 3 and the remainder is 5. Find this number.
Solution.

Let the desired number be $10 x+y$. Then, according to the condition, we have the system $\left\{\begin{array}{l}10 x+y-3=4(x+y), \\ 10 x+y-5=3 x y\end{array} \Rightarrow x=2, y=3\right.$.

Answer: 23.