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To simplify a ratio, find the Greatest Common Divisor (GCD) of all parts and divide each part by it. For 12:18, GCD(12, 18) = 6, so the simplified ratio is 2:3. For three-part ratios like 6:9:12, GCD(6,9,12) = 3, giving 2:3:4.
This simplifier shows the prime factorization of each part so you can see exactly how the GCD is found — the GCD is the product of all prime factors that appear in every part, taken to the lowest power.
A ratio is in its simplest (lowest) form when the GCD of all its parts equals 1. Simplified ratios are easier to work with in proportions, unit rates, and visual comparisons.
Simplified a:b = (a/GCD):(b/GCD) | GCD via prime factorization: product of shared primes at lowest power
Simplify to lowest terms using GCD and prime factorization.
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.