Round #645

What is the greatest common divisor of 36 and 48?

To find the greatest common divisor (GCD) of two numbers, you can use the Euclidean algorithm. Here's how you can implement it in C#: ```csharp using System; class Program { static void Main() { int num1 = 36; int num2 = 48; int gcd = GCD(num1, num2); Console.WriteLine("The greatest common divisor of " + num1 + " and " + num2 + " is: " + gcd); } static int GCD(int a, int b) { while (b != 0) { int temp = b; b = a % b; a = temp; } return a; } } ``` When you run this program, it will output: ``` The greatest common divisor of 36 and 48 is: 12 ```

To find the greatest common divisor (GCD) of two numbers, you can use the Euclidean algorithm. This algorithm is efficient and involves a series of division steps in which the divisor in each step becomes the dividend in the next step, and the remainder becomes the new divisor. The process continues until the remainder is zero. The divisor at that step will be the GCD. Here's how you can implement this in C#: ```csharp using System; public class GCDExample { public static void Main() { int num1 = 36; int num2 = 48; int gcd = CalculateGCD(num1, num2); Console.WriteLine($"The greatest common divisor of {num1} and {num2} is {gcd}"); } public static int CalculateGCD(int a, int b) { while (b != 0) { int temp = b; b = a % b; a = temp; } return a; } } ``` ### Explanation: 1. **Main Method**: This is the entry point of the program where we define two numbers (`num1` and `num2`) and call the `CalculateGCD` method to find their GCD. 2. **CalculateGCD Method**: This method implements the Euclidean algorithm to calculate the GCD. - We use a `while` loop that continues until `b` becomes zero. - Inside the loop, we swap the values of `a` and `b`, and update `b` to be the remainder of `a` divided by `b`. - When `b` is zero, `a` contains the GCD. This implementation is straightforward and follows the Euclidean algorithm efficiently. The use of a simple loop ensures that the code is both clear and performant.