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The largest positive integer that divides two or more integers without leaving a remainder.
Use our verified, free in-browser Fraction Calculator to run scenarios and export PDF reports.
Also known as the Highest Common Factor (HCF), the GCD is fundamental in fraction simplification, modular arithmetic, and cryptography (such as RSA public key generation).
The Euclidean Algorithm calculates the GCD in logarithmic time by repeatedly computing remainders: gcd(a, b) = gcd(b, a mod b) until the remainder is 0.
Euclidean reduction relation where the GCD of two numbers equals the GCD of the divisor and remainder.
First integer.
Second integer.
Scenario: Finding the GCD of 48 and 18 using the Euclidean Algorithm