What is the Greatest Common Factor?
The steps to finding the Greatest Common Factor are hidden in its name. Can you guess what they are? Let’s find out together!
Author
Amber Watkins
Published:
Oct 2024
Key takeaways
- • One of the most important reasons to learn how to find the greatest common factors in math is to use it to reduce fractions.
- • How to find the Greatest Common Factor, or the GCF, can be easily remembered by writing its name backward. The steps are find the factors, choose the ones that are common, and select the greatest.
- • Using an online math app can help your child get the needed practice finding the GCF and other fourth and fifth-grade math skills.
There are a few times in math that we get to work backward. When we do it is always fun! What are we solving? Problems with Greatest Common Factors. You will sometimes see it called the GCF.
Table of contents
What is the Greatest Common Factor (GCF)?
As the name suggests, it involves three steps:
Step 1: Identifying the Factors of two numbers.
Step 2: Discovering which factors are Common.
Step 3: Comparing the Common factors to see which one is the Greatest, or highest in value.
If you read those highlighted words starting with Step 3 backward to Step 1, what does it say? You guessed it: Greatest Common Factors!
The Greatest Common Factor definition says when comparing the factors two numbers have in common there will be one factor that is also the greatest in value. This number is called the greatest common factor, or the GCF.
Let’s take a closer look at the Greatest Common Factor definition by answering three questions:
1. What are Factors?
2. What are Common Factors?
3. How to determine the Greatest Common Factor?
What are Factors?
Factors are the numbers you multiply to get an answer. For example, what are the factors of 12?
To get 12, you can multiply 1 x 12, 2 x 6, or 3 x 4. So those numbers would be factors of 12.
Question: What are the factors of 12?
Answer: The factors of 12 are the numbers 1, 2, 3, 4, 6, and 12.
What are Common Factors?
Common factors are factors that both numbers share. You will find the same number in both lists of factors. For example, the factors for 6 are 1 , 2, 3 and 6. The factors for 12 are the numbers 1, 2, 3, 4, 6, and 12.
Question: What are the Common factors of 6 and 12?
Answer: Since both numbers have 1, 2, 3, and 6 as factors, they are the common factors.
How to Find the Greatest Common Factor
Begin by writing Greatest Common Factor on your paper backward. It should look like this:
- Factors
- Common
- Greatest
Now we have the steps of how to find the greatest common factor:
First, find the factors of the two numbers.
Next, circle the factors that both lists have in common.
Finally, select the factor that is the greatest in value.
Let’s listen in to the following conversation as a teacher explains how to find the greatest common factor of 10 and 15 for one of her students.
Teacher: “Today we will find the greatest common factor of 10 and 15. On your paper can you list all of the factors of 10?”
Student: “Yes, 1 x 10 equals 10 and 2 x 5 equals 10.
So, 1, 2, 5, and 10 are all the factors of 10.”
Teacher: “Perfect, and what about 15, what are the factors of 15?”
Student: “1 x 15 and 3 x 5. So 1, 3, 5, and 15 are factors of 15.”
Teacher: “In those two lists do you see any numbers in common?”
Student: “Yes, 1 and 5.”
Teacher: “So looking at both numbers, which do you think is the Greatest common factor?”
Student: “5.”
You can see how easy it is to find the GCF as long as you follow those three steps. Now it’s your turn to practice.
Practice questions
Question: What is the Greatest Common Factor of 4 and 6?
To find the answer, start by listing the steps on your paper: Factors, Common, Greatest. Then solve!
Answers:
Factors: Factors of 4: 1, 2, 4; factors of 6: 1, 2, 3, 6
Common: Factors that are common: 1, 2
Greatest: Greatest Common Factor: 2
When will you need to find GCF?
In order to simplify or reduce fractions in math, you need to divide the numerator and denominator by their GCF.
Practice Problems
Click on the boxes below to see the answers!
6 is the GCF.
- First find the factors of 18: 1 x 18, 2 x 8, and 3 x 6.
- Second order them from least to greatest 1, 2, 3, 6, and 18.
- Next, find the factors of 24: 1 x 24, 2 x 12, 3 x 8, 4 x 6.
- Order them from least to greatest: 1, 2, 3, 4, 6, 12, and 24
- Next circle the factors from both lists that are found in both: 1, 2, 3, and 6
Finally, out of the factors you circled, which number is the greatest? 6
12 is the GCF
- First find the factors of 48: 1 x 48, 2 x 24, 3 x 16, and 4 x 12, and 6 x 8.
- Second order them from least to greatest: 1, 2, 3, 4, 6, 8, 12, 24, and 48.
- Next, find the factors of 36: 1 x 36, 2 x 18, 3 x 12, 6 x 6, 4 x 9.
- Order them from least to greatest: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- Next circle the factors from both lists that are found in both: 1, 2, 3, 4, 6, and 12.
Finally, out of the factors you circled, which number is the greatest? 12.
4 is the GCF.
- First find the factors of 16: 1 x 16, 2 x 8, 4 x 4.
- Second order them from least to greatest 1, 2, 4, 8, and 16.
- Next, find the factors of 12: 1 x 12, 2 x 6, 3 x 4.
- Order them from least to greatest: 1, 2, 3, 4, and 12.
- Next circle the factors from both lists that are found in both: 1, 2, 4.
Finally, out of the factors you circled, which number is the greatest?
FAQs About Greatest Common Factors
GCF stands for greatest common factor. The greatest common factor is the factor that is common to two numbers that is also the greatest in value.
You find the greatest common factor by finding the factors of two numbers, then comparing the factors to find which are common to both, finally you select the factor that is the greatest or highest in value.
GCF is a comparison of factors, or numbers that are multiplied to get an answer. LCM is a comparison of multiples, or the answers you get when counting by a number. GCF is finding the greatest factor, but LCM is finding the smallest multiple.
