Prime Factorization Calculator
Break a number into its prime factors, and check whether it’s prime.
Every calculation runs locally in your browser.
Prime factorization
2^3 × 3^2 × 5
360 is composite (not prime).
For informational and educational purposes only — not professional or technical advice, and not a substitute for consulting a qualified professional about your specific situation. TrueMeasureKit is not liable for decisions made based on these results. See our Terms of Service.
Why √n is where the search can stop
This checks candidate divisors starting at 2, dividing them out repeatedly whenever they fit, and moving to the next candidate once they don't. It only needs to test candidates up to the square root of whatever remains — if no factor up to that point divides evenly, whatever's left over cannot be composite (it would need a factor pair with one number at or below the square root), so it must be prime itself. Every positive integer greater than 1 has exactly one prime factorization — this is the Fundamental Theorem of Arithmetic, and it's why "prime" numbers are considered the basic building blocks of all whole numbers.
Frequently asked questions
Why does every number have a unique prime factorization?
This is the Fundamental Theorem of Arithmetic: every integer greater than 1 can be represented as a product of primes in exactly one way (ignoring order) — which is why prime factorization is such a foundational tool in number theory and cryptography.