Prime Factorization Calculator

Prime Factorization

About Prime Factorization

Prime factorization is the process of finding which prime numbers multiply together to make the original number. Every whole number greater than 1 can be written as a unique product of prime numbers.

Examples:

  • 12 = 2 × 2 × 3 = 2² × 3
  • 18 = 2 × 3 × 3 = 2 × 3²
  • 30 = 2 × 3 × 5
  • 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5
  • 100 = 2 × 2 × 5 × 5 = 2² × 5²
  • 144 = 2 × 2 × 2 × 2 × 3 × 3 = 2⁴ × 3²

Uses of Prime Factorization:

  • Finding the Greatest Common Factor (GCF)
  • Finding the Least Common Multiple (LCM)
  • Simplifying fractions and radicals
  • Cryptography and computer security

Method:

  1. Start with the number you want to factor
  2. Divide by the smallest prime number (2, 3, 5, 7, 11, ...)
  3. Continue dividing by prime numbers until the result is 1
  4. Write the original number as a product of all the prime factors found