7.3. In a three-digit number, the first digit was crossed out to obtain a two-digit number. If the original number is divided by the obtained number, the quotient is 8 and the remainder is 6. Find the original number.
Answer: 342. Solution. Let $a$ be the first digit of the original number, and $b$ be the two-digit number formed by the last two digits. According to the condition, $100 a+b=8 b+6 \Leftrightarrow 7 b=2(50 a-3)=2 \cdot 49 a+2(a-3)$. Thus, the number $a-3$ must be divisible by 7. Considering that $0<a \leq 9$, we get that $a=3$. Then $b=42$.