Prime Factorisation Calculator
Break a number into prime factors, list all divisors, and test whether it is prime.
Formula
trial division up to √n
Tips
- Every whole number above 1 has exactly one prime factorisation — that is the fundamental theorem of arithmetic.
- Trial division only needs to reach √n: any factor above the square root pairs with one below it.
- 1 is not prime. It has only one divisor, and treating it as prime would break unique factorisation.
Frequently asked questions
Why is factoring large numbers slow?
Trial division scales with √n. That difficulty is not an accident of this tool — the presumed hardness of factoring very large semiprimes is what RSA encryption rests on.