Prime Factorization Calculator

    Find the prime factorization of any number. Break down composite numbers into their prime factors with detailed step-by-step solutions.

    Prime Factorization Calculator

    Enter a positive integer greater than 1

    About Prime Factorization

    Prime factorization is the process of expressing a composite number as a product of prime numbers. This fundamental concept in number theory has applications in cryptography, computer science, and mathematics.

    Key Concepts

    • Prime Number: A number greater than 1 with exactly two factors: 1 and itself
    • Composite Number: A number with more than two factors
    • Fundamental Theorem: Every integer > 1 has a unique prime factorization
    • Factor Tree: Visual method to find prime factors

    Methods

    • Trial Division: Divide by primes in order (2, 3, 5, 7, ...)
    • Factor Tree: Break number into factors repeatedly
    • Pollard's Rho: Advanced algorithm for large numbers
    • Fermat's Method: For numbers close to perfect squares

    Applications

    • Cryptography: RSA encryption relies on factoring difficulty
    • Computer Science: Hash functions and algorithms
    • Mathematics: GCD, LCM, and fraction simplification
    • Number Theory: Understanding number properties

    Examples

    • 12 = 2² × 3
    • 30 = 2 × 3 × 5
    • 100 = 2² × 5²
    • 60 = 2² × 3 × 5

    First 25 Prime Numbers

    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

    Related Tools