Prime Factorization Calculator
Break any integer into its prime factors — with step-by-step solution.
About this calculator
Prime factorization expresses a number as a product of primes. Useful for GCD/LCM, fraction simplification, and number theory.
How prime factorization works
Trial division starts with the smallest prime (2) and repeatedly divides the number whenever it's divisible, then moves on to 3, 5, 7, and so on. The Fundamental Theorem of Arithmetic guarantees that every integer greater than 1 has a unique prime factorization (ignoring order). Prime factorization is the foundation for simplifying fractions, finding the greatest common divisor (GCD), and the least common multiple (LCM).