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