Prime Factorization Game
Prime factorization is a way of breaking down a whole number into its prime factors. Think of it as finding the “prime number building blocks” that you can multiply together to get the original number.
A prime number is a whole number greater than 1 that has only two factors: 1 and itself. Examples are 2, 3, 5, 7, 11, and so on. A composite number is a whole number that has more than two factors.
 
To find the prime factorization of a number, you repeatedly divide it by the smallest prime numbers possible until you are left with only prime numbers. Scroll down the page if you need a more detailed explanation.
 
This Prime Factorization Game allows you to enter the upper bound of the number to customize the difficulty of the game. If you get stuck, don’t worry! The game will provide a detailed, step-by-step solution to help you learn the process.
 

Prime Factorization

Find all the prime factors of a number.

Find factors for numbers up to:

Enable 60-Second Timer

Start Game

Prime Factorization

Time: 60

Score: 0 / 0

Find the prime factors of:

84

Here's how to solve it:

Check Next

Back to Menu

 

How to Play the Prime Factorization Game
The game is designed to help you practice your prime factorizing skills in a fun environment.
Here’s how to play:

1. Find prime factors for 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 a number at the top of the box. Your goal is to find all the prime factors of that number.
   
4. Enter Your Answer: Type your answers into the box. Separate each number by a comma. The factors can entered in any order.
   
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.
   
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 Prime Factorization
Find the Prime Factors of a Number Lesson
To find the prime factorization of a number, you repeatedly divide it by the smallest prime numbers possible until you are left with only prime numbers.
Let’s use an example to walk through the process. We’ll find the prime factorization of the number 72.
Step 1: Start with the smallest prime number.
The smallest prime number is 2. Can you divide 72 by 2? Yes.
72÷2=36
Step 2: Continue dividing by the smallest prime number.
Now we have 36. Can we divide 36 by 2? Yes.
36÷2=18
Step 3: Keep going until you can’t divide by that prime number anymore.
We still have 18. Can we divide 18 by 2? Yes.
18÷2=9
Step 4: Move to the next smallest prime number.
We now have 9. Can we divide 9 by 2? No, it would leave a remainder.
The next smallest prime number is 3. Can we divide 9 by 3? Yes.
9÷3=3
Step 5: Stop when you have a prime number.
The last number we have is 3, which is a prime number. This means we are finished. The prime factors we found are all the numbers we used to divide: 2, 2, 2, 3, and 3.
You can write the prime factorization of 72 as:
2×2×2×3×3=72
 

The video gives a clear, step-by-step approach to walk through the process of finding the prime factorization of a number.

• Show Video

 

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