GCF stands for Greatest Common Factor. Factors are numbers multiplied together, and the result is called the product. Sometimes, it’s necessary to know the GCF of 2 or more numbers. Why? I’m glad you asked. Basically, the GCF helps to efficiently and quickly reduce fractions. One way to determine the GCF is simply by listing the factors. Later, we’ll learn the prime factorization method.

When to use: to reduce fractions
Skills needed: multiplication facts

Method - Naming or Listing Factors

Example: 12 & 36 - Find the GCF

Factors for 12: 1, 2, 3, 4, 6, 12
Factors for 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

What are the common factors? 1, 2, 3, 4, 6, 12
Which common factor is the largest? 12
Thus, the GCF for 12 & 36 is 12.

Question: How do you list factors without missing one?
Let’s redo the above example in more detail.

Name factors of 12
Start with the factor “1.” Write “1” to the left and the 2nd factor, “12” to the right with space between the two numbers. Then ask is “2” a factor of 12. If so, write 2 to the left and the matching factor, “6” to the left. Continue this pattern until 2 numbers listed from the left and right are in sequential order whether they were used as a factor or not.

Factors of 12
1-------------12
1, 2---------6, 12
1, 2,3------4, 6, 12
Note: “3” and “4” are in sequential order. All factors have been listed when this happens.

Factors of 36
1-----------------36
1, 2, ---------------18, 36
1, 2, 3, ------------------12, 18, 36
1, 2, 3, 4-----------------9, 12, 18, 36
1, 2, 3, 4, X---------------9, 12, 18, 36
1, 2, 3, 4, X, 6--------------9, 12, 18, 36
1, 2, 3, 4, X, 6, X-------------9, 12, 18, 36
1, 2, 3, 4, X, 6, X, X-----------9, 12, 18, 36

Note: the “X” represents numbers that are not factors. The bold “X” represents “8.” The number across from it is “9.” Since the numbers are in sequential order, all the factors for 36 have been found.

Application
Reduce the fraction, 12/36.
1. Find the GCF (We know that the GCF for 12 & 36 is 12)
2. Divide the numerator and denominator by 12. (12/12 and 36/12)
3. Thus 12/36 = 1/3