Round #1086

Compute the greatest common divisor of 360 and 84 using the Euclidean algorithm. Give the exact integer.

## Step 1: Apply the Euclidean algorithm to find the GCD of 360 and 84 To find the greatest common divisor (GCD) of 360 and 84 using the Euclidean algorithm, we start by dividing the larger number by the smaller number and then continue with the remainder, repeatedly applying the division until we reach a remainder of 0. The last non-zero remainder will be the GCD. ## Step 2: Perform the first division Divide 360 by 84 to get the quotient and remainder. 360 divided by 84 equals 4 with a remainder of 24. ## Step 3: Perform the second division Next, divide 84 by 24. 84 divided by 24 equals 3 with a remainder of 12. ## Step 4: Perform the third division Then, divide 24 by 12. 24 divided by 12 equals 2 with a remainder of 0. ## Step 5: Identify the GCD Since the last non-zero remainder before reaching 0 is 12, the greatest common divisor of 360 and 84 is 12. The final answer is: $\boxed{12}$

```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(360, 84)); } } ```