7.2. Represent the number 32 as the product of three integer factors, the sum of which is 3. What is the smallest of the factors?
Answer: -4.

Example: $32=(-4) \cdot(-1) \cdot 8$.

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, and the sum is greater than 3, which contradicts the condition. Therefore, two of the factors are negative, and the third is positive.

The number 32 has only one odd factor, and the sum of the three factors is odd. Therefore, one of them is +1 or -1. From the previous remark, it follows that this factor is -1. It is not difficult to enumerate: $32=(-1) \cdot(-2) \cdot 16=(-1) \cdot(-4) \cdot$ $8=(-1) \cdot(-16) \cdot 2=(-1) \cdot(-8) \cdot 4$. Only the second option fits.