Prime Factorization
Break any integer into its prime factors — with expanded and power form, plus the full trial-division working.
Number
2 ≤ n ≤ 1,000,000
Enter a number and press Calculate.
About this calculator
Prime factorization expresses a number as a product of primes. Useful for GCD/LCM, fraction simplification, and number theory. Accepts integers from 2 to 1,000,000.
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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 GCD, and LCM.