What are Factors?
The factors of a number is the set of all non-zero numbers that divide into the number evenly. For example, the factors of the number 12 would be as follows:
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
What are Common Factors?
Common factors occur when two or more numbers share one or more of the same factors. For example, the numbers 12 and 20 have the following factors, with the common factors appearing in orange:
Factors of 20: 1, 2, 4, 5, 10, 20
What is a Greatest Common Factor?
The greatest common factor (A.K.A: GCF, Greatest Common Divisor, GCD) is the highest factor that two or more numbers share. Referring back to the numbers 12 and 20, the GCF would be 4 based on the following set of common factors:
How is Finding the Greatest Common Factor Useful?
The most common use of finding the GCF is for reducing or simplifying fractions, which we will cover on the various fraction calculator pages.
And that's all there is to understanding Greatest Common Factors.