Prime factorization calculator
Enter a whole number above 1 to get its unique prime factorization, such as 360 = 2³ × 3² × 5. Handy for homework, simplifying roots and finding GCD and LCM.
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How to use it
- Enter number.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
n = p1^e1 × p2^e2 × p3^e3 and so on, found by repeated division by small primes, then Pollard rho for large factors. Number of divisors = the product of (e + 1) over every exponent.
Example
Inputs: Number = 360. Result: Prime factorization: 2³ × 3² × 5; Distinct prime factors: 3; Number of divisors: 24.
Limits and caveats
- Accepts whole numbers from 2 to 10^15.
- Zero, 1 and negative numbers have no prime factorization in the usual sense.
Questions about this tool
Is the prime factorization unique?
Yes. By the fundamental theorem of arithmetic every number above 1 has exactly one factorization into primes, ignoring order.
How do I get the number of divisors from it?
Add 1 to each exponent and multiply. For 360 = 2³ × 3² × 5 that is (3+1)(2+1)(1+1) = 24 divisors.
What if the result is the number itself?
If the number appears alone, it is prime, like 97.