Euclidean algorithm
What is the Euclidean Algorithm?
The Euclidean Algorithm is an ancient and elegant method for finding the Greatest Common Divisor (GCD) of two numbers. It works by repeatedly dividing the larger number by the smaller one and taking the remainder until the remainder becomes zero. This algorithm is incredibly efficient and forms the basis for many mathematical operations.
Key Components:
1. Two positive integers
2. Division operation
3. Remainder tracking
4. Iterative process
Core Rules:
1. Divide larger number by smaller number
2. Replace larger number with smaller number
3. Replace smaller number with remainder
4. Repeat until remainder is zero
5. Last non-zero number is the GCD
Basic Process:
GCD(a,b) where a ≥ b
1. Divide a by b
2. If remainder is 0, b is the GCD
3. If remainder exists, repeat with b and remainder