How To Find The GCF – Teaching GCF With Examples

Key concepts of How To Find The GCF

The greatest common factor is the largest factor that a set of numbers share. Approach teaching GCF with caution: students often confuse GCF contexts with LCM (least common multiple) contexts. GCF scenarios require students to arrange groups, distribute an item equally, or make smaller sections of something. LCM problems tend to be more common and include instances of repeating events where something happens simultaneously. 

One strategy to find the GCF is to list all of the factors of a set of numbers and identify the largest common factor. 

Another strategy is to divide the set of numbers by common factors until you end up with prime numbers. Next, multiply the common factors and there you have it: the GCF. 

How do you teach the greatest common factor? 

To find the GCF, list the factors of each number. Remind students that factors are numbers that can divide evenly into a given number without leaving a remainder. Coach your students to arrange the listed factors from least to greatest. Prompt students to circle the common factors before identifying the greatest common factor. 

Another way to find the GCF is with a ladder model. First, put the set of numbers inside the ladder. Then, divide the numbers by a common factor. Repeat this process until your set of numbers are prime. Last step: calculate the GCF by multiplying the common factors outside of the ladder.

Listing Factors 

Step 1: Find all of the factors of each number. 

Start out by directing your students to list all of the factors of each number. Ask your students what would make more sense: randomly listing the factors or arranging them from least to greatest. Stamp for students that listing the factors from least to greatest will help them better keep track of their work. 

Step 2: Circle the common factors. 

Direct your students to circle all of the common factors. These are the factors you see in both factor lists. 

Step 3: Identify the GCF.  

Ask students to identify the largest common factor. 

Ladder Method

Step 1: Put the set of numbers inside the ladder model. 

Step 2: Identify a common factor that can divide evenly into both numbers and simplify. 

Step 3: Repeat this process until you are left with prime numbers. 

Step 4: Multiply the common factors to find the GCF.

Examples

Example 1: Listing Factors (18 and 24)

Example 2: Ladder Method (18 and 24)

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Step 1: Identify a common factor that can divide evenly into both numbers and simplify. 

Step 2: Repeat this process until you are not left with any common factor.

Step 3: Multiply the common factors to find the GCF.

Why teach the greatest common factor this way?

Listing factors from least to greatest helps students to organize their thinking. Using the ladder method allows students who do not have strong fluency to still master this essential skill. 

Using Byte’s practice problems and virtual manipulatives will give your students the chance to make mistakes, get feedback, and try again until they master this essential concept!  

Also read: How To Teach Applying Distributive Property [Examples Included]

Vocabulary for teaching the greatest common factor 

Factor: A whole number that divides exactly into another number with no remainder.

Common Factor: Whole numbers that are a factor for two different sets of numbers.

Prime Number: The only factors of a prime number are 1 and the number itself.

Greatest Common Factor: The largest of all the factors that are common to two or more numbers or polynomials.

Misconceptions and errors students are likely to have:

• Students might multiply the outside number by the first term only. For example, students could simplify the expression 2 (3x + 4) as 6x + 4. Name the error and provide your students with grid paper. Direct your students to model each group of the terms inside the parentheses, then ask as the terms are being repeated about the relationship. Stamp that the outside number multiplies each set of terms inside the parentheses. 

Resources: 

• Downloadable worksheet for practicing greatest common factor 
• Quiz for assessing greatest common factor 

Frequently Asked Questions On How To Find GCF?