The LessonThe greatest common factor in algebra is the largest factor that is common to two or more terms.
Understanding the Greatest Common Factor in AlgebraA factor is a quantity that divides exactly into a term. It is one of the numbers, letters and brackets (or a product of them) that are multiplied together to make a term. For example,
The greatest common factor is the largest collection of numbers and letters that make up both terms. In our example, 2x is the greatest common factor.
2x is the largest term that divides exactly into both original terms (2xy and 2xz).
2xy ÷ 2x = y
2xz ÷ 2x = z
What's in a Name?The Greatest Common Factor (GCF) is so called because it is the largest (greatest) factor that is the same (common) to the numbers. It may sometimes be called:
- Greatest Common Divisor (GCD)
- Highest Common Factor (HCF)