Round #1057

Compute the greatest common divisor of 252 and 198 using the Euclidean algorithm. Give the exact integer.

## Step 1: Apply the Euclidean algorithm to find the GCD of 252 and 198 To find the greatest common divisor (GCD) of 252 and 198 using the Euclidean algorithm, we start by dividing the larger number by the smaller number and then continue the process with the remainder. ## Step 2: Perform the first division Divide 252 by 198 to get the quotient and remainder. 252 = 198 * 1 + 54. ## Step 3: Continue the Euclidean algorithm with the previous divisor and remainder Now, divide 198 by 54. 198 = 54 * 3 + 36. ## Step 4: Continue the algorithm with the previous divisor and remainder Next, divide 54 by 36. 54 = 36 * 1 + 18. ## Step 5: Continue the algorithm with the previous divisor and remainder Then, divide 36 by 18. 36 = 18 * 2 + 0. ## Step 6: Determine the GCD Since the remainder is now 0, the divisor from this last division is the GCD. Therefore, the GCD of 252 and 198 is 18. The final answer is: $\boxed{18}$

```csharp using System; public class Program { public static int Gcd(int a, int b) { while (b != 0) { int temp = b; b = a % b; a = temp; } return a; } public static void Main() { Console.WriteLine(Gcd(252, 198)); } } ``` This C# program uses the Euclidean algorithm to compute the greatest common divisor (GCD) of two numbers, 252 and 198. The GCD function takes two integers as input and returns their GCD. The algorithm works by repeatedly replacing 'a' and 'b' with 'b' and the remainder of 'a' divided by 'b' until 'b' is zero. At that point, 'a' is the GCD. The result is then printed to the console. The output will be 18.