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 the difficulty of factoring very large numbers is what RSA encryption relies on. 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, 4, 5 and so on; a composite divisor such as 4 never divides, because its prime factors have already been removed. Each successful division strips out one prime factor, and the search stops once the divisor squared exceeds what is left: anything above 1 that remains at that point is itself prime. The result lists the factors and writes them as a product of prime powers.

Input matters here: factorization is defined for whole numbers above one, so the calculator rounds a decimal down and drops a minus sign (84.9 and -84 are both factored as 84), and 0 or 1 gives no result. Type the number without commas. 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.