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:

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.