Factoring Fundamentals
What Is a Factor?
A factor is a number or expression that is multiplied by another to make a product. Understanding factors is the first step toward factoring algebraic expressions and quadratics.
What are factors?
The factors of a whole number divide it exactly, with no remainder. They usually come in pairs: because 3 × 4 = 12, both 3 and 4 are factors of 12. The pair 1 and 12 works too.
How to find factors
- Start with 1 and the number itself.
- Test each whole number in order.
- When a number divides exactly, record it and its partner.
- Stop after the pairs begin to repeat.
Worked example
Find the factors of 18
- 1 × 18 = 18
- 2 × 9 = 18
- 3 × 6 = 18
The factors of 18 are 1, 2, 3, 6, 9, and 18.
Common mistakes
- Forgetting 1 and the number itself.
- Listing multiples, such as 18, 36, and 54, instead of factors.
- Missing the partner in a factor pair.
Practice more
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