Prime factorisation calculator
Break a number into prime factors and count its divisors.
Fill in the fields and the result will appear here automatically.
Factor an integer from 2 to 1000000000000 into primes and read its power notation, number of distinct primes and positive-divisor count. Factors of 2 are removed first; odd candidates are then tested up to the square root of the current remainder. Any remainder greater than one is included as a prime factor. The factorization is unique up to the order of the factors.
How it works
Formula and logic
Trial division runs up to the square root of the number; whatever is left above one is itself prime.
Example
360 = 2³ · 3² · 5, giving (3+1)(2+1)(1+1) = 24 divisors. Removing factors of 2 leaves 45; removing factors of 3 leaves 5, which is included as the remaining prime.
Fields and units
- Number — unitless
How to use
- — Enter a whole number of two or more.
- — Read the factorisation.
- — Check the divisor count if you need it.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: definition and uniqueness of prime factorization
- Limitation
- Factor an integer from 2 to 1000000000000 into primes and read its power notation, number of distinct primes and positive-divisor count.
FAQ
How is the divisor count obtained?
Multiply each exponent increased by one. For 2³ · 3² · 5 that is 4 × 3 × 2 = 24.
Why can I not factorise one?
This page starts at 2. One has no prime factors; its factorization can be represented by the empty product, equal to 1. One is not prime: a prime has exactly two distinct positive divisors.
Is there an upper limit?
This page accepts n ≤ 10¹². The bound limits trial-division cost. It is not where Number integers start losing precision: the general safe-integer bound is 9007199254740991.
How do I know a number is prime?
Its factorisation is the number itself and the calculator says so on a separate line.