To understand Common Factor, we must understand the words:

Once we understand these words, we are ready to understand Common Factors.  So, lets look at the words and learn their meaning:

Common - Shared by all, belonging equally to two or more places. (examples: 3, and 9 are common to the lists {1,3,5,7,9,11} and {3,6,9,12,15} )

Factors - Numbers that can be multiplied together to obtain a given number are called factors.  (example: 2 and 5 are factors of 10 because 2X5 = 10)

Now, let's look at the phase Common Factors.

Common Factor

Given the numbers 21 and 24

      21  = 3 x 7

      24 = 3 x 8

      3 is a common factor of 21 and 24.

 

Given the numbers 36 and 44

      36 = 4 x 9

      44 = 4 x 11

       4 is a common factor of 36 and 44.

 

Given the numbers 8 and 12,

        8 = 2 x 4

        12 = 2 x 6

        2 is a common factor of 8 and 12.

 

Given the numbers 8 and 12,

        8 = 4 x 2

        12 = 4 x 3

        4 is a common factor of 8 and 12.

 

Notice in the number pairs 8 and 12, depending on your choice of ways to factor 12, you can find different "common factors" for the two numbers.   This isn't unusual.   Many number pairs have multiple common factors, depending on how you factor the numbers.