I Greatest Common Divisor Finder Algorithm

The Greatest Common Divisor (GCD) Finder Algorithm is a mathematical method that aims to find the largest positive integer that divides two or more integers without leaving a remainder. This algorithm is extremely useful in various applications, such as simplifying fractions, solving Diophantine equations, and determining the least common multiple (LCM) of two numbers. One of the most popular and efficient algorithms for computing the GCD of two integers is the Euclidean Algorithm, which is based on the principle that the GCD of two numbers remains the same if the larger number is replaced by its difference with the smaller number. The Euclidean Algorithm repeatedly applies the subtraction process until the two numbers become equal, which is the GCD of the original numbers. Alternatively, the algorithm can also be implemented using the modulo operation, making it more efficient in terms of execution time. The idea is to keep calculating the remainder when the larger number is divided by the smaller number until the remainder becomes zero. The last non-zero remainder in this process is the GCD of the given numbers. This approach is often preferred in programming and computational applications due to its efficiency and simplicity, making the Greatest Common Divisor Finder Algorithm an essential tool in number theory and various real-world applications.
namespace Algorithms.Numeric.GreatestCommonDivisor
{
    /// <summary>
    /// TODO.
    /// </summary>
    public interface IGreatestCommonDivisorFinder
    {
        /// <summary>
        /// Finds greatest common divisor for numbers a and b.
        /// </summary>
        /// <param name="a">TODO.</param>
        /// <param name="b">TODO. 2.</param>
        /// <returns>Greatest common divisor.</returns>
        int Find(int a, int b);
    }
}

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