Enter a whole number to find its prime factorization.
How to Use the Prime Factorization Calculator
One whole number in, its full prime factorization out — no need to specify how many factors to look for.
Every whole number above 1 breaks down into exactly one set of prime factors — not "one of several possible sets," exactly one, regardless of which order you find them in. That's the Fundamental Theorem of Arithmetic, and it's the reason 12 is always 2² × 3 and never anything else.
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5This Prime Factorization Calculator finds that breakdown by trial division: testing 2, then 3, then each candidate upward, dividing it out as many times as it fits before moving on — and stopping once the candidate passes the square root of whatever's left, since any factor bigger than that would already have shown up paired with a smaller one.
Small-scale, this feeds into finding GCF and LCM and reducing fractions. At large scale, it's the whole basis of RSA encryption — the security comes directly from how computationally painful it is to factor the product of two enormous primes back apart.