Problem 9.1. Find the largest five-digit number, the product of whose digits is 120.
Answer: 85311.

Solution. The largest single-digit divisor of the number $120-8$, so the desired number definitely starts with this digit. The product of all the remaining digits is 15.

The largest single-digit divisor of the number $15-5$, so the digit in the thousands place will be this digit. The product of the last three digits is three 3, so the largest number will end with 311.