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.

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