Greatest Common Factor Game
The Greatest Common Factor (GCF) is the largest number that divides evenly into two or more numbers. It’s also sometimes called the Greatest Common Divisor (GCD).
The GCF is the “biggest” factor that two or more numbers share. It’s a fundamental concept used for simplifying fractions and solving other math problems.
 
To find the Greatest Common Factor (GCF) of two numbers, you can list all the factors for each number and identify the largest number that appears in both lists. Alternatively, you can use prime factorization, where you break down each number into its prime factors and then multiply the prime factors that are common to both. Scroll down the page for a more detailed explanation.
 
This Greatest Common Factor Game allows you to enter the upper bound of the numbers to customize the difficulty of the game. If you get stuck, don’t worry! The game will provide a detailed, step-by-step solution using the prime factorization method to help you learn the process.
 

Greatest Common Factor

Find all the prime factors of a number.

Find factors for numbers up to:

Enable 60-Second Timer

Start Game

Greatest Common Factor

Time: 60

Score: 0 / 0

Find the prime factors of:

84

Here's how to solve it:

Check Next

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How to Play the Greatest Common Factor Game
The game is designed to help you practice your prime factorizing and factoring skills in a fun environment.
Here’s how to play:

1. Use numbers up to: Enter a number to indicate the upper bound of the numbers.
   
2. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
3. Look at the Problem: You’ll see two numbers at the top of the box. Your goal is to find the greatest common factor of the two numbers.
   
4. Enter Your Answer: Type your answer into the box.
   
5. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown how to get the correct answer using prime factorization.
   
6. Get a New Problem: Click the Next button (or press Enter again) for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
7. Back to Menu Click “Back to Menu” to restart the game.
    
   

How to Find the Greatest Common Factor
Greatest Common Factor Lesson
There are a couple of ways to find the GCF. The most straightforward method is to list all the factors of each number and find the largest one they have in common.
Listing Factors
Let’s find the GCF of 12 and 18.

1. List the factors of the first number.
   The factors of 12 are all the numbers you can multiply to get 12:
   Factors of 12: 1,2,3,4,6,12
   
2. List the factors of the second number.
   The factors of 18 are:
   Factors of 18: 1,2,3,6,9,18
   
3. Find the common factors.
   The numbers that appear in both lists are the common factors:
   Common factors: 1,2,3,6
   
4. Find the greatest common factor.
   The largest number in the list of common factors is 6.
   So, the GCF of 12 and 18 is 6.
    
   

Using Prime Factorization
For larger numbers, listing all the factors can be difficult. A more efficient method is to use prime factorization.
Here’s how it works using the same example, 12 and 18:

1. Find the prime factorization of each number.
   12=2×2×3
   18=2×3×3
   
2. Identify the prime factors they have in common.
   Both numbers share a 2 and a 3.
   
3. Multiply the common prime factors.
   2×3=6
   The result is the same: the GCF of 12 and 18 is 6. This method is particularly useful for finding the GCF of larger numbers or for three or more numbers.
    
   

The video gives a clear, step-by-step approach to walk through the process of using prime factorization to find the GCF of a pair of numbers.

• Show Video

 

Free Factor Games Online
Factor Finder Game	Prime Factorization Game	Greatest Common Factor Game

 

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Learning Fractions	Equivalent Fractions	Compare Fractions
Simplify Fractions	Greatest Common Factor	Least Common Multiple
Improper Fractions & Mixed Numbers	Add Fractions	Subtract Fractions
Subtract Fractions from Whole Numbers	Multiply Fractions	Divide Fractions
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Subtract Mixed Numbers	Multiply Mixed Numbers	Divide Mixed Numbers

 

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