Use List Method to Find GCF (2025)

Thegreatest common factor, also known as GCF, of two numbers is the largest number that can evenly divide the given two numbers.

Another way to define GCF: The greatest common factor of two numbers is the largest factor that is common to both numbers.

The two definitions above mean the same thing.

Don’t be confused if you encounter other names of the greatest common factor. They all have the same meaning. The alternate names of GCF are:

  • Greatest Common Divisor which is abbreviated as GCD
  • Highest Common Factor which is abbreviated as HCF
Use List Method to Find GCF (1)

Before you continue, make sure that you know how to find all the factors of a number. Otherwise, please review my short lesson on how to find all factors of a number using the rainbow method.

Use List Method to Find GCF (2)

Steps on How to Find the Greatest Common Factor

Step 1: List or write ALL the factors of each number.

Step 2: Identify the common factors. You can do that by encircling each common factor or drawing a line segment between them. It’s really up to you how you want to mark the common factors so they stand out.

Step 3: After identifying the common factors, select or choose the number which has the largest value. This number will essentially be the Greatest Common Factor (GCF).

Examples of How to Find the Greatest Common Factors

NOTE: I decided to focus on finding the GCF of two numbers because they are the most common problems that you will encounter when studying GCF.

Example 1: Find the Greatest Common Factor of [latex]12[/latex] and [latex]18[/latex].

This problem is easy because the numbers involved are relatively simple. You should be able to find all the factors of 12 and 18 using the rainbow method. As an alternative, I have listed all the factors of numbers from 1 to 100 for you to use at your own convenience.

So here are all the factors of both [latex]12[/latex] and [latex]18[/latex].

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

Use List Method to Find GCF (3)

After listing all the factors of each number, we now identify the common factors. As you can see below, the common factors of [latex]12[/latex] and [latex]18[/latex] are [latex]1[/latex], [latex]2[/latex], [latex]3[/latex], and [latex]6[/latex]. Notice that I identified the common factors by enclosing them in a “rectangle”.

Use List Method to Find GCF (4)

So what is the GCF then? Obviously, the GCF is one of the common factors. The common factor which has the largest value is actually the Greatest Common Factor. Therefore the GCF of [latex]12[/latex] and [latex]18[/latex] is [latex]6[/latex]. That’s it!

Use List Method to Find GCF (5)

Example 2: Find the Greatest Common Factor of [latex]64[/latex] and [latex]96[/latex].

In many instances in math, as the number becomes larger, the level of difficulty of the problem also increases. Yes, this is true as well when finding the GCF of two large numbers. However, the concept or procedure never changes.

So here we go. Let’s find the complete factors of [latex]64[/latex] and [latex]96[/latex].

◉ The complete factors of [latex]64[/latex] are 1, 2, 4, 8, 16, 32, and 64.

◉ While the complete factors of [latex]96[/latex] are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

Below are the lists of factors in a vertical format.

Use List Method to Find GCF (6)

The next step is to compare the lists of factors. Then draw a shape so that the common factor is inside each shape. You can be creative here! Notice that on the illustration below, we have six (6) common factors which are [latex]1[/latex], [latex]2[/latex], [latex]4[/latex], [latex]8[/latex], [latex]16[/latex], and [latex]32[/latex].

Use List Method to Find GCF (7)

By looking at the common factors, the one which has the biggest value is [latex]32[/latex]. Therefore, the greatest common factor of [latex]64[/latex] and [latex]96[/latex] is simply [latex]32[/latex].

Use List Method to Find GCF (8)

Example 3: Determine the Greatest Common Factor of [latex]42[/latex] and [latex]126[/latex].

It is easy to rush into solving a math problem because you are already familiar with the steps on how to work it out. However, it is a good practice to pause or step back and look at the problem from a broader perspective before delving into the process of solving the problem itself.

The reason is, that the procedure that you already know may not be the most time-efficient because there might be a better way, that is, a shorter solution.

Let’s approach it this way. If [latex]42[/latex] can divide [latex]126[/latex] without a remainder, then it implies that [latex]42[/latex] is a factor of [latex]126[/latex]. Not only that [latex]42[/latex] is a common factor of [latex]42[/latex] and [latex]126[/latex], but it is also the common factor that has the highest value.

If you think about it, it is not possible to have a common factor greater than [latex]42[/latex] because it cannot be more than the smaller number of the given two numbers.

So, does [latex]42[/latex] divide [latex]126[/latex] evenly? The answer is yes! Therefore, the greatest common divisor (GCD) of [latex]42[/latex] and [latex]126[/latex] is simply [latex]42[/latex]. Done!

Example 4: What is the GCF of [latex]71[/latex] and [latex]223[/latex] ?

Just like with example #3, don’t jump into the motion of applying the steps that you already know. I can’t overemphasize the importance of practicing restraint when solving math problems in general. Stepping back to see the big picture is extremely important because this will allow you to strategize and therefore be able to devise a viable approach to the problem.

So now, if you closely examine the two numbers which are [latex]71[/latex] and [latex]223[/latex], you should easily recognize that both of them are prime numbers. Remember that a prime number has exactly two factors which are [latex]1[/latex] and itself. In other words, we can say that a prime number is only divisible by [latex]1[/latex] and itself.

Listing the factors of [latex]71[/latex] and [latex]223[/latex]:

Factors of 71: 1, 71

Factors of 223: 1, 223

We should be able to conclude that since [latex]1[/latex] is the ONLY common factor, it implies that [latex]1[/latex] must also be the greatest common factor by default. Thus, [latex]{\rm{gcf}}\left( {71,223} \right) = 1[/latex].

Example 5: What is the GCF of [latex]72[/latex] and [latex]84[/latex] ?

First, we know that both numbers are not prime, in fact, both are even numbers. It means they have common factors other than [latex]1[/latex]. Secondly, it is obvious too that the smaller number [latex]72[/latex] cannot evenly divide the larger number [latex]84[/latex]. This leaves us to conclude that the smaller of the two numbers, [latex]72[/latex], is NOT the greatest common factor either.

Well, the only option left is to proceed with the step-by-step procedure of finding the GCF of two numbers as discussed in the first part of this lesson.

Listing all the factors of each number, we have:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Use List Method to Find GCF (9)

Comparing the lists of factors, the common factors of 72 and 84 are 1, 2, 3, 4, 6, and 12.

Use List Method to Find GCF (10)

Taking it from the diagram, [latex]12[/latex] is the greatest common factor of [latex]72[/latex] and [latex]84[/latex]. Done!

Use List Method to Find GCF (11)

You may also be interested in these related math lessons or tutorials:

Use Prime Factorization to Find GCF

Finding LCM using the List Method

Use Prime Factorization to Find LCM

Use List Method to Find GCF (2025)

FAQs

Use List Method to Find GCF? ›

One way to find the GCF is to make lists of the factors for two numbers and then choose the greatest factor that the two factors have in common. Find the GCF for 12 and 16. It is helpful to order them from smallest to largest in order to make sure that you cover every factor.

How to get GCF by listing method? ›

GCF by Listing out the Factors (List Method) In this method, we write down all the factors/divisors of a group of numbers. After listing down the divisors, we pick the greatest number that commonly divides the said numbers without leaving any remainder.

How to find GCF using list of factors? ›

To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.

How to do the listing method? ›

Listing Method

This method involves writing the members of a set as a list, separated by commas and enclosed within curly braces. For example, the four seasons are a set and could be written as {Summer, Autumn, Spring, Winter}. Note: The order of the elements in the list doesn't matter.

How to find GCF step by step? ›

Find the Greatest Common Factor of Two or More Expressions
  1. Factor each coefficient into primes. Write all variables with exponents in expanded form.
  2. List all factors—matching common factors in a column. ...
  3. Bring down the common factors that all expressions share.
  4. Multiply the factors.

What is the method used to find the GCF? ›

To find the greatest common factor of two or more natural numbers, there are 3 methods that can be used - listing out of the common factors, prime factorization, and division method. Each method requires division and multiplication to obtain the GCF. For example, the GCF of 14 and 35 is 7.

What is the listing factor method? ›

The listing method involves the process of listing the factors of the given numbers. For example, find the HCF of 20 and 35. The common factors of the given numbers are : 1,2,4,5,10,20. The greatest among all other numbers is 20, so it shall be the HCF of both the numbers.

How do you use the GCF factoring method? ›

How to factor the greatest common factor from a polynomial.
  1. Find the GCF of all the terms of the polynomial.
  2. Rewrite each term as a product using the GCF.
  3. Use the “reverse” Distributive Property to factor the expression.
  4. Check by multiplying the factors.
May 26, 2022

What are the steps to finding the GCF of a list of Monomials? ›

Note: To find the greatest common factor (GCF) between monomials, take each monomial and write it's prime factorization. Then, identify the factors common to each monomial and multiply those common factors together. Bam!

What is the GCF of 8 and 12 using the listing method? ›

GCF of 8 and 12 by Listing Common Factors

There are 3 common factors of 8 and 12, that are 1, 2, and 4. Therefore, the greatest common factor of 8 and 12 is 4.

What is the GCF of 9 and 12 using the listing method? ›

GCF of 9 and 12 by Listing Common Factors

There are 2 common factors of 9 and 12, that are 1 and 3. Therefore, the greatest common factor of 9 and 12 is 3.

How to get GCF using listing method? ›

The first strategy involves simply listing the factors of each number, and then looking for the greatest factor that is shared by both numbers. For example, if we are looking for the GCF of 36 and 45, we can list the factors of both numbers and identify the largest number in common. The GCF of 36 and 45 is 9.

What is the rule method of listing method? ›

The listing method is the method in which the members of the set are written as a list, separated by the comma and enclosed within the curly braces. Rule method in sets involves specifying the rule or a condition that can be used to decide whether an object can belong to the set.

What is the GCF of 24 and 36 listing method? ›

The GCF of 24 and 36 is 12. To calculate the GCF (Greatest Common Factor) of 24 and 36, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 24 and 36, i.e., 12.

What is the GCF of 24 and 36 using the listing method? ›

FAQs on GCF of 24 and 36

The GCF of 24 and 36 is 12. To calculate the GCF (Greatest Common Factor) of 24 and 36, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 24 and 36, i.e., 12.

What is the GCF of 6 and 8 using the listing method? ›

What is the GCF of 6 and 8? The GCF of 6 and 8 is 2. To calculate the greatest common factor (GCF) of 6 and 8, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 8 = 1, 2, 4, 8) and choose the greatest factor that exactly divides both 6 and 8, i.e., 2.

What is the GCF of 15 and 20 using the listing method? ›

The GCF of 15 and 20 is 5. To calculate the GCF (Greatest Common Factor) of 15 and 20, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 15 and 20, i.e., 5.

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