Prime Factorisation Calculator — Free and Exact
Break a number down into the primes it is built from.
Runs on your device What you paste is processed by your own browser. It is never sent to a server, and it is not stored anywhere after you leave the page.
Short answer
Any whole number from 2 up to 10^12 can be factorised into primes for free in a web browser. The factors are found by trial division up to the square root of the number and shown grouped into powers, so 360 comes back as 2^3 × 3^2 × 5. A number with no factors but itself is labelled prime. Several numbers can be factorised at once, one per line.
At a glance
| Accepts | One whole number per line, 2 to 10^12 |
|---|---|
| Produces | The number as a product of prime powers |
| Processing | In your browser |
| Price | Free, no limits |
| Account | Not required |
Every whole number above 1 has exactly one prime factorisation — that is the fundamental theorem of arithmetic, and it is why there are no options on this page. There is nothing to choose, only the answer.
The factors are grouped into powers because 2 × 2 × 2 × 3 × 3 × 5 and 2^3 × 3^2 × 5 say the same thing and only one of them can be read at a glance. The upper limit of 10^12 is where trial division stops being instant: factorising larger numbers needs an algorithm whose runtime is worth warning someone about, and an honest refusal beats a frozen tab.
How to use it
- 1
Type your numbers
One whole number per line, each 2 or greater.
- 2
Convert
Each number comes back as a product of primes, grouped into powers.
- 3
Read the primes
A number with no smaller factors is marked as prime rather than written as a product of itself.
- 4
Copy the result
Copy to the clipboard, or download it as a text file.
Frequently asked questions
What is the largest number it can factorise?
10^12. Above that, trial division would need more than a million steps per number and the page would appear to hang, so it declines instead.
How do I know whether a number is prime?
Factorise it. If the answer is the number itself, marked prime, then it has no divisors other than 1 and itself.
Why does it refuse 1 and 0?
Because neither has a prime factorisation. 1 is a unit — it is not prime and has no prime factors — and 0 is divisible by everything.
What are prime factors actually used for?
Reducing fractions, finding a least common denominator, simplifying surds, and checking divisibility. They are also the foundation of RSA, whose security rests on factorisation being hard for numbers vastly larger than anything this page accepts.