1. The 6 -digit number $739 A B C$ is divisible by 7,8 , and 9 . What values can $A, B$, and $C$ take?
1. Since $\operatorname{gcd}(7,8,9)=1$, then $739 A B C$ is divisible by 7,8 , and 9 iff it is divisible by $7 \cdot 8 \cdot 9=$ 504. Note that the only integers between 739000 and 739999 which are divisible by 504 are 739368 and 739872. So, $(A, B, C) \in\{(3,6,8),(8,7,2)\}$.