Prime Factorization Calculator

Find the prime factorization of any number. Free online prime factor calculator with factor tree.

The Prime Factorization Calculator breaks down any positive integer into its prime factors—the building blocks of all numbers. See the complete factorization as a product of primes and understand the unique prime representation of any number. Essential for finding GCD, LCM, simplifying fractions, and understanding number properties.

Common use cases

  • Simplifying fractions
  • Finding GCD and LCM
  • Cryptography fundamentals
  • Number theory studies
  • Divisibility analysis

How to use

  1. Enter a positive integer
  2. Click factorize for prime factors
  3. View the factor tree visualization
  4. See the prime factorization
  5. Identify repeated prime factors

FAQ

What is prime factorization?

Writing a number as a product of prime numbers. Example: 60 = 2² × 3 × 5 = 2×2×3×5.

Is prime factorization unique?

Yes, the Fundamental Theorem of Arithmetic states every integer > 1 has a unique prime factorization (ignoring order).

How is this used for GCD?

GCD uses the lowest power of common primes. For 12=2²×3 and 18=2×3², GCD=2×3=6.

What if the number is prime?

A prime number's factorization is just itself. For example, 13 = 13.