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Greatest Common Divisor (GCD) Calculator

Calculate the GCD (also known as Highest Common Factor or HCF) for two or more integers with step-by-step Euclidean divisions.

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Greatest Common Divisor (GCD)

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Understanding GCD (HCF)

The Greatest Common Divisor (GCD), also called the Highest Common Factor (HCF), of two or more non-zero integers is the largest positive integer that divides each of the numbers without leaving a remainder. Finding the GCD is a fundamental skill in arithmetic, used for reducing fractions to their simplest forms, finding common denominators, and resolving scheduling/tiling grids. The most efficient way to compute GCD is the **Euclidean Algorithm**, which recursively divides the larger number by the smaller one until the remainder becomes zero.

FAQ

What is the Euclidean Algorithm?
It is an ancient, highly efficient mathematical algorithm for computing the greatest common divisor of two integers. It works by repeatedly replacing the larger number by its remainder when divided by the smaller number, until the remainder is zero. The last non-zero remainder is the GCD.
Can I calculate the GCD of more than two numbers?
Yes! The GCD of multiple numbers is computed iteratively. E.g. for numbers A, B, and C, we first calculate the GCD of A and B, let's call it G1. Then we calculate the GCD of G1 and C, which gives the final GCD of all three numbers.
What happens if the GCD is 1?
If the GCD of two numbers is 1, they are called **coprime** or **mutually prime** numbers. This means they share no common divisors other than 1.

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