Given a three-digit number ABB, the product of its digits is a two-digit number AC, the product of the digits of this number equals C (here, as in mathematical puzzles, the digits in the number notation are replaced by letters; identical letters correspond to identical digits, different letters correspond to different digits). Determine the original number.

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Think about what $A$ is equal to.

## Solution

From the condition of the problem, it is clear that $A C=C$; then $A=1$ and $B B=10+C$, where $C$ is a digit. The last equation has a unique solution $B=4, C=6$. Therefore, the required number is 144.

## Answer

144.