Golovanov A.S.

The numbers from 1 to 10 are divided into two groups such that the product of the numbers in the first group is divisible by the product of the numbers in the second group.

What is the smallest value that the quotient of the first product divided by the second can have?
Among the numbers from 1 to 10, only the number 7 is divisible by 7. Therefore, it must be included in the first group, and the quotient is no less than 7.

For example, when it equals $7:(3 \cdot 5 \cdot 6 \cdot 7 \cdot 8):(1 \cdot 2 \cdot 4 \cdot 9 \cdot 10)$.

## Answer

7.