GCD Calculator
Calculate the greatest common divisor (GCD) of two numbers using the Euclidean algorithm.
Gcd Val
12
Formula
## Greatest Common Divisor (GCD) ### Definition The GCD of two numbers is the largest positive integer that divides both numbers evenly. ### Euclidean Algorithm 1. Divide the larger number by the smaller 2. Replace the larger number with the remainder 3. Repeat until the remainder is 0 4. The last nonzero remainder is the GCD ### Relationship with LCM **LCM(a, b) = |a × b| / GCD(a, b)**
Exemplo Resolvido
Find GCD(48, 36).
- 0148 = 1 × 36 + 12
- 0236 = 3 × 12 + 0
- 03GCD = 12
- 04LCM = (48 × 36) / 12 = 144
Perguntas Frequentes
What is the GCD?
The greatest common divisor (also called highest common factor or HCF) is the largest number that divides two numbers without leaving a remainder.
How is GCD used?
GCD is used to simplify fractions (divide numerator and denominator by their GCD), solve Diophantine equations, and in cryptography (RSA algorithm).
What if one number is zero?
GCD(a, 0) = a for any positive integer a. The GCD of zero and any number is that number itself.
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