Online Free Prime Factorization Calculator
Prime Factorization Calculator
Prime Factorization Calculator
What is Prime Factorization?
Prime factorization is the process of finding which prime numbers multiply together to make the original number. Every integer greater than 1 either is a prime number itself or can be represented as a product of prime numbers.
Why is it Important?
Prime factorization is fundamental in number theory and has practical applications in cryptography, computer science, and solving various mathematical problems like finding the greatest common factor (GCF) and least common multiple (LCM).
How to Find Prime Factors?
Start with the smallest prime number (2) and divide the original number by it. If it divides evenly, 2 is a prime factor. Continue dividing by 2 until it no longer divides evenly, then move to the next prime number (3), and so on.
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Enter a number and click "Calculate" to see its prime factorization and other properties.
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How to Use ThisPrime Factorization Calculator
- Enter a positive integer greater than 1 in the input field
- Click “Calculate” or wait for automatic calculation
- View the results in different visualization modes
- Explore factor pairs and step-by-step breakdown
- Use the GCF/LCM tab for comparing two numbers
- Try batch processing for multiple numbers
Keyboard Shortcuts
- Enter – Calculate factorization
- Ctrl+R – Generate random number
- Ctrl+C – Copy results
- Ctrl+H – Show history
What Prime Factorization Means
Prime factorization is the process of expressing a number as a product of prime numbers (numbers greater than 1 that have no divisors other than 1 and themselves).
For example:
- 12=2×2×312 = 2 \times 2 \times 3
- 60=2×2×3×560 = 2 \times 2 \times 3 \times 5
How to Do Prime Factorization
Here’s a simple method:
- Start with the smallest prime (2). Divide the number by 2 until it’s no longer divisible.
- Move to the next prime (3, 5, 7, …). Keep dividing until it’s no longer divisible.
- Repeat until the quotient is 1. The factors you collected are the prime factorization.
Example Walkthrough
Let’s factorize 84:
- 84÷2=4284 \div 2 = 42 → factor: 2
- 42÷2=2142 \div 2 = 21 → factor: 2
- 21÷3=721 \div 3 = 7 → factor: 3
- 77 is prime → factor: 7
So:
84=2×2×3×7=22×3×784 = 2 \times 2 \times 3 \times 7 = 2^2 \times 3 \times 7
Why It’s Useful
- Cryptography (RSA encryption relies on prime factorization difficulty).
- Mathematics (finding greatest common divisors, least common multiples).
- Pattern recognition (prime structure reveals properties of numbers).