GCD Calculator
Calculate the Greatest Common Divisor of multiple numbers
Understanding GCD
The Greatest Common Divisor (GCD) of two or more numbers is the largest positive integer that divides each of them without leaving a remainder. It's also known as the Greatest Common Factor (GCF) or Highest Common Factor (HCF).
Key Concepts
- GCD is always positive
- GCD(a,b) ≤ min(|a|, |b|)
- If GCD(a,b) = 1, a and b are coprime
- GCD can be found using prime factorization
Common Uses
- Simplifying fractions
- Solving Diophantine equations
- Cryptography algorithms
- Computer graphics scaling
Euclidean Algorithm
This calculator uses the Euclidean algorithm, which is based on the principle that the GCD of two numbers also divides their difference. It's one of the oldest algorithms still in use today.