The concepts of greatest common factor and the least common multiple are frequently mixed up! It is important to understand the difference between the two.

The word greatest implies that your answer will be larger than the two numbers you started with,...but this is untrue!

A common factor is any number that can be evenly divided into two or more given numbers.

Example: Let us find all of the common factors of 24 and 30 and highlight them in red.

24 - 1 , 2 , 3 , 4 , 6 , 12 , 24

30 - 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30

All of the red numbers are common factors of 24 and 30.

Out of the highlighted numbers, 6 is the greatest of the values. Therefore 6 is the GCF or greatest common factor of 24 and 30.