Prime Factorization Calculator
Find the prime factorization of any positive integer up to 10^15. Returns factors in ascending order with exponent notation.
Inputs
Prime factorization
—
Exponent notation
—
Is it prime?
—
Distinct primes
—
Total factors
—
About Prime Factorization Calculator
Fundamental theorem of arithmetic
Every integer > 1 has a unique prime factorization (up to order). 360 = 2³ × 3² × 5 — no other combination of primes multiplies to 360.
How long it takes
Trial division (used here) is fast for numbers up to ~10⁹. Beyond that, advanced algorithms (Pollard rho, ECM, quadratic sieve) are needed. RSA security relies on the difficulty of factoring 2048+ bit numbers — far beyond this calculator.
Uses
Simplifying fractions (divide by GCD). Cryptography (RSA, Diffie-Hellman). Number theory problems. Finding divisors (combinations of prime factors).