What Is the Greatest Common Factor?

What Is the Greatest Common Factor?

The greatest common factor is the largest factor that is common to two or more numbers.

Understanding the Greatest Common Factor

The numbers that multiply together to make another number are its factors.

2 is a factor of 4 because 2 × 2 = 4:

4 = 2 times 2

2 and 3 are factors of 6 because 2 × 3 = 6:

6 = 2 times 3

The greatest common factor is the largest number that is a factor for both numbers.

In our example, 2 is the greatest common factor.

2 is the greatest common factor of 4 and 6

Another way of thinking about a factor is as a number which divides exactly into another number.

2 is the largest number that divides exactly into 4 and 6.

4 ÷ 2 = 2

6 ÷ 2 = 3

See Also

What is a factor? What is the greatest common factor in algebra?