Round #636

What is 7 factorial (7!)?

To calculate 7 factorial (7!), you multiply all positive integers from 1 to 7 together: \[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] Let's compute this step by step: \[ 7 \times 6 = 42 \] \[ 42 \times 5 = 210 \] \[ 210 \times 4 = 840 \] \[ 840 \times 3 = 2520 \] \[ 2520 \times 2 = 5040 \] \[ 5040 \times 1 = 5040 \] So, \( 7! = 5040 \).

To calculate 7 factorial (7!), you can use a simple iterative approach in C#. Factorial of a number \( n \) is the product of all positive integers less than or equal to \( n \). Here's how you can implement it: ```csharp using System; class Program { static void Main() { int number = 7; long factorial = CalculateFactorial(number); Console.WriteLine($"{number}! = {factorial}"); } static long CalculateFactorial(int n) { if (n < 0) throw new ArgumentException("Number must be non-negative."); long result = 1; for (int i = 2; i <= n; i++) { result *= i; } return result; } } ``` ### Explanation: 1. **Main Method**: This is the entry point of the program where we define the number for which we want to calculate the factorial (in this case, 7) and call the `CalculateFactorial` method. 2. **CalculateFactorial Method**: - It takes an integer `n` as input. - It checks if `n` is negative and throws an `ArgumentException` if it is, since factorials are not defined for negative numbers. - It initializes a variable `result` to 1 (since the factorial of 0 is 1). - It uses a `for` loop to multiply `result` by each integer from 2 up to `n`. - Finally, it returns the calculated factorial. This implementation is straightforward and efficient for calculating factorials. The use of `long` ensures that the result can handle large values without overflow, as factorials grow very quickly.