Prime Factorization Calculator
Break a positive integer down into its prime factors — with exponential form (2^3 x 3^2 x 5), a flat product, a factor/exponent table, the count of distinct primes, and every divisor.
Input
Output
| Prime | Exponent |
|---|---|
| No data yet | |
Guides
The Prime Factorization Calculator breaks any positive integer down into the prime numbers that multiply together to make it. Enter a number like 360 and it returns the prime factorization in exponential form — 2^3 × 3^2 × 5 — along with the expanded product, a factor/exponent table, the number of distinct primes, and a full list of divisors.
What is prime factorization?
Every integer greater than 1 is either a prime number or can be written as a unique product of primes. This is the Fundamental Theorem of Arithmetic. For example, 360 factors as 2 × 2 × 2 × 3 × 3 × 5, usually written more compactly as 2^3 × 3^2 × 5. Because the factorization is unique, it is the fingerprint of a number and the starting point for computing greatest common divisors, least common multiples, and reduced fractions.
How to use it
- Type a positive whole number into the Number field.
- The results update instantly — no button to press.
- Copy any single result, or download the factor table (CSV) and the divisor list (text).
The calculator reports:
- Prime factorization — the primes with their exponents, e.g.
2^3 × 3^2 × 5. A prime input is labelled(prime). - Expanded — the same factorization written out as a flat product, e.g.
2 × 2 × 2 × 3 × 3 × 5. - Distinct prime factors — how many different primes appear.
- Factors — a table pairing each prime with its exponent.
- All divisors — every number that divides the input evenly, in ascending order.
Edge cases
- 1 has no prime factors — it is the empty product, neither prime nor composite. Its only divisor is 1.
- Prime inputs factor to just themselves (97 →
97 (prime)), with divisors 1 and the number itself. - 0 and negative numbers are rejected: prime factorization is only defined for positive integers, and 0 is divisible by every integer so it has no unique factorization.
How large a number can it handle?
Inputs are accepted up to 9,007,199,254,740,991 (about 9 × 10^15). The math runs on BigInt, so every digit is exact — there is no floating-point rounding even for large results. Factoring uses trial division up to the square root of the number, which is fast for everyday inputs; a very large number whose largest prime factor is itself huge (a big semiprime) can take a moment longer.
Is my input sent anywhere?
No. The calculation runs entirely in your browser — the number you enter never leaves your device.