D. The GCF – Greatest Common Factor

Greatest common factors are used regularly to simplify the organization of people (such as student-to-teacher ratios) and things (for example, fair distribution of various items into food hampers).

Greatest Common Factor
the largest factor that is common to two or more numbers

   

Example 1

Using prime factorization, determine the greatest common factor of 24 and 36.

Prime Factorization of 24

Prime Factorization of 36

Match identical prime factors.

The numbers 2, 2, and 3 are prime factors of both 24 and 36.

So, the GCF = 2 × 2 × 3 = 12.

In Example 1, the greatest common factor of 24 and 36 was shown to be 12. Note that there are other common factors, such as 4 and 6, but 12 is the greatest common factor.

The following instructional video demonstrates how factor trees can be used to determine the GCF of larger numbers:

 

 As with many concepts in math, there are a number of ways of showing how to determine a GCF. You will see a different approach in Unit 5. It is important that you show your work in the way that makes the most sense to you, even if that means it looks a little different from what you have seen here in Example 1.