Prime Factorization Calculator
This tool has been used … times.
Enter any integer of 2 or above to factor it into primes instantly. See the step-by-step division process, and check whether a number is prime. Free, no sign-up.
Supports positive integers from 2 up to about 9 quadrillion. Very large primes may stop the calculation.
How to Use
- Enter a Number
- Type an integer of 2 or above (up to about 9 quadrillion) into the input field. The prime factorization result appears automatically. Very large primes that take too long will stop the calculation.
- View Calculation Steps
- Click “Show Steps” to expand the step-by-step division process. If the number itself is prime, it will be identified as a prime number.
- Copy / Share the Result
- Use “Copy Result” to copy the result to your clipboard. Use “Post” to share it on X (Twitter).
Frequently Asked Questions
What is the prime factorization of 56?
56 = 2 × 2 × 2 × 7, or 2³ × 7 in exponent form. Likewise, 28 = 2² × 7 and 6084 = 2² × 3² × 13². Enter any integer above to factor it instantly with the division steps shown.
How do I do prime factorization?
Divide by the smallest primes in order: divide by 2 as many times as possible, then 3, then 5, and so on until the quotient reaches 1. For example, 60 divides by 2 twice, by 3 once, and by 5 once, so 60 = 2² × 3 × 5. Click “Show Steps” in this tool to see the same process.
How can I tell if a number is prime?
A prime number is divisible only by 1 and itself, and it is hard to tell by sight: 91 looks prime but equals 7 × 13, while 89 really is prime. This tool identifies primes automatically, so you can also use it as a prime checker.
What is prime factorization used for?
Simplifying fractions (finding the greatest common divisor), calculating the least common multiple, and simplifying square roots (for example, √56 = 2√14). Shared prime factors give you the GCD, and all prime factors combined give you the LCM.