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