How To Factor Negative Numbers

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.

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:

\(\begin{aligned}
1 × -8 &= -8 \
-1 × 8 &= -8 \
2 × -4 &= -8 \
-2 × 4 &= -8
\end{aligned}\)

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.