Factoring Fundamentals
Common Factors
Common factors are factors shared by two or more numbers. Finding them helps you simplify numbers and identify what can be taken outside an algebraic expression.
What is a common factor?
A number is a common factor when it divides every number in the group exactly. For example, 3 divides both 6 and 9, so 3 is a common factor of 6 and 9.
How to find common factors
- List the factors of each number.
- Compare the lists.
- Keep every number that appears in all of them.
Worked example
Common factors of 12 and 18
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
The common factors are 1, 2, 3, and 6.
Common mistakes
- Keeping a factor that appears in only one list.
- Looking only for the greatest common factor when the question asks for all common factors.
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