Prime Factorization Calculator
Break down any positive integer into its prime factors with this free calculator. See the complete factorization with exponents, list of unique primes, total divisor count, and primality check.
Prime factorization is the process of expressing a positive integer as a product of prime numbers. Every integer greater than 1 is either a prime number or can be uniquely represented as a product of primes (the Fundamental Theorem of Arithmetic).
How Prime Factorization Works:
Start by dividing the number by the smallest prime (2) as many times as possible. Then try the next prime (3), then 5, 7, 11, and so on. Continue until the remaining quotient is 1.
For example, 360 = 2^3 x 3^2 x 5. This means 360 = 2 x 2 x 2 x 3 x 3 x 5 = 8 x 9 x 5 = 360.
Applications:
Prime factorization is fundamental in number theory, cryptography (RSA encryption relies on the difficulty of factoring large numbers), finding GCD and LCM, simplifying fractions, and solving divisibility problems.