Greatest Common Divisor (GCD) Calculator
Find the greatest common divisor of two or more numbers.
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Find the Greatest Common Divisor (GCD) of Any Set of Numbers
Our GCD Calculator quickly finds the greatest common divisor for a set of numbers using the Euclidean algorithm and also calculates the Least Common Multiple (LCM).
What is a GCD Calculator?
A Greatest Common Divisor (GCD) Calculator is a mathematical tool that finds the largest positive integer that can divide a set of numbers without leaving a remainder. It's a fundamental concept in number theory, often used for simplifying fractions and solving problems in modular arithmetic. This calculator also finds the Least Common Multiple (LCM) as part of its analysis.
How It Works: The Euclidean Algorithm
To find the GCD of two numbers, the calculator uses the efficient Euclidean algorithm, which is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.
Frequently Asked Questions
What is the Greatest Common Divisor (GCD)?
The Greatest Common Divisor (GCD) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. It is also known as the Greatest Common Factor (GCF).
How do you find the GCD?
The most efficient method for finding the GCD is the Euclidean algorithm. It works by repeatedly replacing the larger number with the remainder of the division of the larger number by the smaller one, until the remainder is zero. The last non-zero remainder is the GCD. Our calculator uses this algorithm.
What is the GCD of 120 and 300?
The GCD of 120 and 300 is 60. You can use our calculator to see the step-by-step calculation using the Euclidean algorithm.
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