Prime Factorization Calculator

The Prime Factorization Calculator breaks down any number into its prime factors. Whether you’re working on a math problem, verifying results, or generating a factor tree, this tool gives you clean output instantly. You can choose whether to show steps and display results in standard or exponent form.

It’s simple, fast, and handles one or many numbers line-by-line perfect for students, teachers, and anyone needing clear prime factorizations.

How to Use:

Enter one number per line in the Input Numbers box. For example:

12
84
91
100

Results appear live in the Prime Factors output box.

You can adjust how the results are formatted using these toggles:

• Show steps prepends the original number (e.g., 84 = 2 × 2 × 3 × 7)
• Exponent form groups repeated primes (e.g., 2^2 × 3 × 7)

Click Convert to manually run or just type it updates live. Use Copy to grab results instantly.

What Prime Factorization Calculator can do:

This tool factors whole numbers ≥ 2 into their prime components. It works great for:

• Generating clean prime products
• Showing factorizations for schoolwork
• Creating or checking math worksheet answers
• Practicing mental math or factor trees

If the exponent option is enabled, repeated primes are condensed (e.g., 2 × 2 × 2 becomes 2^3). The result always respects input order and is formatted cleanly.

Example:

Let’s say you input the following list of numbers:

12  
84  
91  
100

With “Exponent form” enabled and “Show steps” off, the output will be:

2^2 × 3  
2^2 × 3 × 7  
7 × 13  
2^2 × 5^2

If you enable “Show steps”, the results update to:

12 = 2^2 × 3  
84 = 2^2 × 3 × 7  
91 = 7 × 13  
100 = 2^2 × 5^2

And if you disable “Exponent form”, it switches to raw prime factor breakdown:

2 × 2 × 3  
2 × 2 × 3 × 7  
7 × 13  
2 × 2 × 5 × 5

This makes it easy to see both the expanded multiplication and the compact exponent format great for teachers, students, or anyone working through factor trees or simplifying math expressions.

Prime Factorization Calculator Table:

This table shows how common numbers are broken down by the calculator.

Common Use Cases:

Use this tool to generate or check prime factorizations. It’s great for assignments, mental math, quizzes, puzzles, and anything else that uses prime products. Teachers love it for showing exponent groupings; students use it for instant clarity.