8.3. Find the largest four-digit number, all digits of which are different, and which is divisible by each of its digits. Of course, zero cannot be used.
Solution: Since the number of digits is fixed, the number will be larger the larger the digits in its higher places are. We will look for the number in the form $\overline{98 a}$. It must be divisible by 9. Therefore, the sum $a+b$ must give a remainder of 1 when divided by 9. At the same time, this sum does not exceed 13, as it consists of different single-digit addends, which are less than 8. Therefore, this sum is either 1 or 10. The largest variant that fits these conditions is 9873, but it does not work since it is not divisible by 8. The next highest in seniority, 9864, clearly works.

Solution: Only proven that the number 9864 works - 2 points. The idea to look for the answer in the form $\overline{98 a b}-1$ - 1 point.