Prime Factorization

Visualize factor trees and explore unique prime factorization with GCD/LCM calculations

Overview

The Prime Factorization tool breaks down numbers into their unique prime factors using visual factor trees. See how every number can be expressed as a product of primes in exactly one way, and use prime factorization to calculate GCD and LCM efficiently.

Tips

  1. Build factor trees step by step: Start with any factor pair and keep breaking down composite numbers until you reach all primes - you’ll always get the same prime factors regardless of which path you take.

  2. Use divisibility rules: Check if a number is divisible by 2 (even), 3 (sum of digits), or 5 (ends in 0 or 5) to quickly identify initial factors.

  3. Compare multiple numbers: Factor several numbers at once to see their shared prime factors, which makes finding GCD (take minimum powers) and LCM (take maximum powers) straightforward.

  4. Start with smallest primes: Always divide by the smallest possible prime (2, 3, 5, 7, 11…) and only test up to the square root of the remaining number.

  5. Express with exponents: Write repeated prime factors using exponent notation (like 2³ × 3²) for a cleaner, more compact representation.