4. Which digit must be substituted instead of the star so that the following large number is divisible by 7 ?
$$
\underbrace{66 \cdots 66}_{2023} \times \underbrace{55 \cdots 55}_{2023}
$$
Solution. Since 111111 is divisible by 7 we need to find the digit that makes $6 \star 5$ divisible by 7 . Such digit is 6 .