Greatest Common Factor
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The Greatest Common Factor (GCF) refers to the largest number or expression that divides two or more numbers (or terms) exactly, without leaving a remainder.
For example:
The GCF of the numbers 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 evenly.
The GCF of the terms 6x^2 and 9x is 3x, because 3 is the largest factor common to both coefficients (6 and 9), and x is the common variable with the smallest power (which is x).
To find the GCF:
List the factors of each number or term.
Identify the largest common factor between them.
In algebra, this process is important for simplifying expressions and factoring polynomials.