8.1. Represent the number 36 as the product of three integer factors, the sum of which is 4. What is the smallest of the factors?
Answer: -4.

Example: $36=(-4) \cdot(-1) \cdot 9$.

Solution. The given factorization is unique. This can be proven.

If all three factors are positive, then the largest of them is not less than 4 (since $3^{3}<36$), and the sum is greater than 4, which contradicts the condition. Therefore, two of the factors are negative, and the third is positive.

Then the positive factor is 9. Indeed, if it is not more than 6, then the sum of the absolute values of the other two is greater than 2; if it is not less than 12, then the sum of the absolute values of the other two is less than 8. Then the two negative factors are either -4 and -1, or -2 and -2. Only the first variant satisfies the condition.