Advanced Euclid's Algorithm GCD Calculator

Calculate Greatest Common Divisor using Euclid's Algorithm with step-by-step visualization and 3D mathematical representations

🔢 GCD Input

Enter numbers to find their Greatest Common Divisor

First Number

Second Number

Multiple Numbers (Optional)

Show detailed algorithm steps

📊 GCD Results

Greatest Common Divisor calculation results

Enter numbers to calculate their Greatest Common Divisor

📈 Algorithm Progression

Visual representation of Euclid's algorithm steps

📊 Factor Analysis

Prime factorization and common factors

Understanding Euclid's Algorithm

Euclid's Algorithm is an efficient method for computing the greatest common divisor (GCD) of two integers. It's based on the principle that the GCD of two numbers doesn't change if the larger number is replaced by its difference with the smaller number.

Algorithm Steps

Repeatedly apply: GCD(a,b) = GCD(b, a mod b) until one number becomes zero. The other number is the GCD.

Time Complexity

The algorithm runs in O(log(min(a,b))) time, making it very efficient even for large numbers.

Applications

Used in cryptography, fraction simplification, and solving Diophantine equations in number theory.

Extended Algorithm

The extended version also finds coefficients x,y such that ax + by = gcd(a,b), useful for modular arithmetic.