By Amy Harris Updated Aug 30, 2022
A constant is a number that contains no variables—such as x or y—and is therefore a plain integer or decimal. (See Reference 1) For example, -7 is a constant, while -7x is not. Because constants are ordinary numbers, factoring them follows the same rules you learned in early math classes: list all pairs of integers that multiply to the given number.
Start with the pair 1 and the constant itself. Since 1 times any number equals that number, this pair is always valid. For instance, factoring -12 yields the pair 1, -12.
Check whether the integer 2 divides the constant evenly. If it does, record the pair 2, -6 for –12. If the constant is not divisible by 2, skip this step. This test is equivalent to asking if there exists an integer k such that 2 × k = constant.
Repeat the process for the integer 3. For –12, 3 divides evenly, producing the pair 3, -4. If the division leaves a remainder, omit this step.
Continue incrementing the divisor until you reach the absolute value of the constant. For –12, the remaining pairs are 4, -3, 6, -2, and 12, -1. The full set of factors for –12 is thus: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12. When factoring a positive integer, you can stop once you encounter repeated pairs—after testing 3 for 12, for example, any further pairs would simply duplicate earlier ones.
When factoring a constant, only consider integer pairs. Every non‑zero integer has at least the trivial factors 1 and the number itself. For instance, 3 factors into just 1 and 3.
