Factors are numbers that -- when multiplied together -- result in another number, which is known as a product. The laws of multiplication state that when a negative number is multiplied by a positive number, the product will be negative. So, if considering a factor pair of a negative product, one of these factors must be negative and the other factor must be positive. Otherwise, factoring negative numbers works in the same way as factoring positive numbers.

### Factors of a Negative Number

The factors of a number entail all of the numbers that can be multiplied by one another to produce that number. For example, the factors of -8 are: 1 and -8, -1 and 8, 2 and -4, and -2 and 4. This is because each of these factor pairs, when multiplied together, produce -8, as follows: 1 x -8 = -8; -1 x 8 = -8; 2 x -4 = -8; and -2 x 4 = -8. Essentially, to factor a negative number, find all of its positive factors, then duplicate them and write a negative sign in front of the duplicates. For instance, the positive factors of -3 are 1 and 3. Duplicating them produces 1, 3, 1, 3; writing a negative sign before the duplicates produces 1, 3, -1, -3, which are all of the factors of -3.