Prime Factorization Calculator

Every whole number greater than one can be written as a product of primes, and this tool finds that unique decomposition for any positive integer you enter. Prime factorization sits at the heart of number theory and cryptography, and it shows up in the algorithms that organize and compress the roughly 250 zettabytes of data the world is expected to produce in 2026. Students, teachers, and working professionals can all use it to turn a tedious hand calculation into an instant result.

Behind the scenes, the method is plain trial division. The number is divided by 2 as many times as it will go, then by 3, then 5, then 7, and so on up through the primes. Each successful division strips out one prime factor; the process stops once the running quotient falls to 1, leaving the full list of factors, which the result expresses as a product of prime powers.

Input matters here: the calculator only accepts positive integers, so decimals or negative values return an error because factorization is defined only for integers above one. Note that 1 is never prime and so never appears in any factorization. The factors can technically be written in any order, but the output lists them from smallest to largest by convention.