Prime Factorization: Methods and Applications
Published Apr 13, 2026 · 6 min read
Prime factorization breaks a number into its prime building blocks. Every integer greater than 1 has a unique prime factorization.
Method 1: Trial Division
Divide by the smallest prime (2), then next (3, 5, 7...) until you reach 1. Example: 360 → 360/2=180, 180/2=90, 90/2=45, 45/3=15, 15/3=5, 5/5=1. So 360 = 2³ × 3² × 5.
Applications
- Finding GCD/LCM — Compare prime factorizations of two numbers
- Simplifying fractions — Cancel common prime factors
- RSA encryption — Security relies on the difficulty of factoring large numbers
- Modular arithmetic — Used in hash functions and checksums
Try it: Use our Prime Factorization Calculator to instantly factor any number.
📚 Sources: Wolfram MathWorld