About This Calculator
This calculator finds the greatest common divisor (GCD) of two or more positive integers. The GCD is the largest positive number that evenly divides all input values without a remainder. It's commonly used in simplifying fractions, number theory, and algebra.
How It Works
- Enter two or more positive integers separated by spaces or commas.
- It uses the Euclidean algorithm: starting with the first two numbers, it applies
GCD(a, b) = GCD(b, a % b)recursively. - The resulting GCD is then used with the next number, continuing until all values are processed.
- The result is displayed along with a factor list table for each number, with the common divisor (GCD) clearly highlighted.
Frequently Asked Questions
What is the greatest common divisor (GCD)?
The GCD is the largest number that divides two or more integers exactly, leaving no remainder. It's also called the greatest common factor (GCF).
Is GCD the same as GCF?
Yes. GCD (Greatest Common Divisor) and GCF (Greatest Common Factor) refer to the same concept. Both identify the largest shared divisor among integers.
How is the GCD calculated?
The calculator uses the Euclidean algorithm, which repeatedly applies the ruleGCD(a, b) = GCD(b, a % b)until the result stabilizes.
Where is GCD used?
GCD is used in simplifying fractions, solving Diophantine equations, finding common denominators, and optimizing integer operations in number theory and cryptography.