Greatest Common Factor (GCF)

The greatest common factor (gcf) between 2 numbers is the largest factor that they have in common. One good way to find this number is to write down all the factors of both numbers and then find the biggest one that appears in both lists.

For example, find the GCF of 12 and 8:

Factors of 12: 1 , 2 , 3 , 4 , 6 , 12
Factors of 8 : 1 , 2 , 4 , 8

The largest factor they both have is 4. This is the greatest common factor (GCF).

There is an equation for finding the GCF if you know the least common multiple (LCM) of your 2 numbers.
Multiply the two numbers together and divide by their LCM:

The GCF of a and b: GCF(a , b) = a x b / LCM (a, b)

For our example of 12 and 8 we have:

GCF (12 , 8) = 12 x 8 / LCM (12 , 8) Since the least common multiple of 12 and 8 is 24, we have:
GCF (12 , 8) = 12 x 8 / 24 = 96/24 = 4 <=== a shorter way!

Now, can you find the GCF of 22 and 33?