Basic GCD Calculator
What is GCD?
The Greatest Common Divisor (GCD) of two or more numbers is the largest positive integer that divides each number without a remainder.
Example: GCD(48, 18) = 6, because 6 is the largest number that divides both 48 and 18.
Multiple Numbers GCD
Visual GCD Representation
Algorithm Performance Comparison
Algorithm Comparison
Euclidean Algorithm: Most commonly used, efficient for most cases. Time complexity: O(log(min(a,b)))
Binary GCD: Uses only subtraction and division by 2. Better for computers. Time complexity: O(log²(min(a,b)))
Prime Factorization: Intuitive but slower for large numbers. Time complexity: O(√min(a,b))
Real-World Applications
Fraction Simplifier
Grid/Pattern Designer
Find the optimal grid size for arranging objects in rows and columns.
Gear Ratio Calculator
Calculate the smallest gear combination for a desired ratio.
Tile Pattern Calculator
Find the largest square tile that can cover a rectangular area evenly.
GCD Practice Quiz
Quick GCD Challenge
Factor Race Game
Find all common factors as quickly as possible!