QUICK LINKS


Introduction

QUICK LINKS


Introduction

Greatest Common Factor (GCF)

INTRO
A factor is a number that fits evenly into a given number.
Factors always come in pairs consisting of the factor and the number of times it fits evenly into the given number.
It's like we're dividing candy up - the factors are the number of people we can divide the candy equally among and the number of pieces each person gets.
Click on the buttons below to see the factors and factor pairs of :
Factors of
:
fits evenly into times.
The Greatest Common Factor (GCF) is the largest factor two or more numbers have in common.
Factors of
Factors of
When we organize the factors from least to greatest, we can easily see that the GCF of and is .

Greatest Common Divisor (GCD)

GCD is the same thing as GCF. It tells us the largest number two or more numbers can be evenly divided by.
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to find the greatest common factor and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

CALCULATOR

GCF Calculator

Find the greatest common factor, or GCF, ofand.

Step 1. Remember what a factor is.

A factor is a number that fits evenly into another number.

Step 4. Find the greatest common factor.

This is the largest factor the two numbers have in common.
Factors of
Factors of
So, the greatest common factor, or GCF, is .
KEY STEPS

How to Find the GCF

Step 1. Remember what a factor is.

A factor is a number that fits evenly into another number.

Step 2. Find the factors of the first number.

We’re looking for every number that fits evenly into the first number.

Step 3. Find the factors of the second number.

We’re looking for every number that fits evenly into the second number.

Step 4. Find the greatest common factor.

This is the largest factor the two numbers have in common.
LESSON
Finding the GCF

Finding the GCF

A factor is a number that fits evenly into a given number.
Factors always come in pairs consisting of the factor and the number of times it fits evenly into the given number.
In other words, factors are pairs of numbers we can multiply together to form a given number.
When we have two or more given numbers, we can compare their factors to see which ones they have in common.
The largest factor they share is called the Greatest Common Factor (GCF).

What is the difference between GCF and LCM?

Greatest Common Factor (GCF)Least Common Multiple (LCM)
Largest factor two or more numbers have in common.Smallest multiple two or more numbers have in common.
Example: GCF of and is .
Factors of :
Factors of :
Example: LCM of and is .
Multiples of :
Multiples of :

GCF & Fractions

We can use the GCF to simplify fractions. All we need to do is find the GCF of the numerator and denominator, and divide both by the GCF.
Let’s walk through step-by-step examples of how to find the GCF of numbers!

EXAMPLE 1

Let's start by finding the GCF of and .

Step 1. Remember what a factor is.

A factor is a number that fits evenly into another number.

Step 4. Find the greatest common factor.

This is the largest factor the two numbers have in common.
Factors of
Factors of
So, the greatest common factor, or GCF, is .

EXAMPLE 2

Nice work! Now, let's find the GCF of and .

Step 1. Remember what a factor is.

A factor is a number that fits evenly into another number.

Step 4. Find the greatest common factor.

This is the largest factor the two numbers have in common.
Factors of
Factors of
So, the greatest common factor, or GCF, is .
Awesome! If you’d like to practice additional problems finding the GCF, expand the
Practice
below before closing out this lesson! ⚡
PRACTICE
Finding the GCF

Practice: Finding the GCF

Question 1 of 10: Find the GCF of 9 and 12.

Step 1. Remember what a factor is.

A factor is

Step 2. Find the factors of the first number.

We’re looking for every number that fits evenly into the first number.
Factors of :

Step 3. Find the factors of the second number.

We’re looking for every number that fits evenly into the second number.
Factors of :

Step 4. Find the greatest common factor.

What is the largest factor the two numbers have in common?
Factors of
Factors of
GCF
Awesome job! The GCF is  .

CONCLUSION
Incredible job, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?