7.5. A set for playing lotto contains 90 barrels numbered with natural numbers from 1 to 90. The barrels are somehow distributed among several bags (each bag contains more than one barrel). We will call a bag good if the number of one of the barrels in it equals the product of the numbers of the other barrels in the same bag (for example, the bag "2, 3, 6" is good, while "4, 5, 10" is not). What is the maximum possible number of good bags?
Answer: 8.

Solution: In each good bag, there are no fewer than three barrels. The smallest number in each good bag must be unique; otherwise, the largest number in this bag would not be less than $10 \times 11=110$, which is impossible. For the same reason, if a good bag contains a barrel with the number 1, it must also contain another barrel with a single-digit number. Therefore, the number of good bags does not exceed 8.

On the other hand, an example can be provided where there are exactly 8 good bags. We can gather 8 good bags $(2,17,34),(3,16,48),(4,15,60),(5,14,70),(6,13,78),(7,12,84),(8$, $11,88)$, and $(9,10,90)$. All other numbers can be placed in a separate bag that is not good.

Criteria: Example only - 3 points.

Estimate only - 3 points.

Noting that each bag must contain a single-digit number - 1 point, can be combined with the example.