diff --git a/api/CourseRegistration.Application/Services/IMathService.cs b/api/CourseRegistration.Application/Services/IMathService.cs
new file mode 100644
index 0000000..5a0c780
--- /dev/null
+++ b/api/CourseRegistration.Application/Services/IMathService.cs
@@ -0,0 +1,16 @@
+namespace CourseRegistration.Application.Services;
+
+/// <summary>
+/// Interface for mathematical utility operations.
+/// </summary>
+public interface IMathService
+{
+    /// <summary>
+    /// Calculates the factorial of a non-negative integer.
+    /// </summary>
+    /// <param name="n">A non-negative integer whose factorial is to be computed.</param>
+    /// <returns>The factorial of <paramref name="n"/> as a <see cref="long"/>.</returns>
+    /// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="n"/> is negative.</exception>
+    /// <exception cref="OverflowException">Thrown when the result exceeds <see cref="long.MaxValue"/>.</exception>
+    long CalculateFactorial(int n);
+}
diff --git a/api/CourseRegistration.Application/Services/MathService.cs b/api/CourseRegistration.Application/Services/MathService.cs
new file mode 100644
index 0000000..89723eb
--- /dev/null
+++ b/api/CourseRegistration.Application/Services/MathService.cs
@@ -0,0 +1,34 @@
+namespace CourseRegistration.Application.Services;
+
+/// <summary>
+/// Provides mathematical utility operations such as factorial calculation.
+/// </summary>
+public class MathService : IMathService
+{
+    // 20! is the largest factorial that fits in a long (Int64)
+    private const int MaxFactorialInput = 20;
+
+    /// <summary>
+    /// Calculates the factorial of a non-negative integer iteratively.
+    /// </summary>
+    /// <param name="n">A non-negative integer (0 – 20) whose factorial is to be computed.</param>
+    /// <returns>The factorial of <paramref name="n"/>.</returns>
+    /// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="n"/> is negative.</exception>
+    /// <exception cref="OverflowException">Thrown when <paramref name="n"/> exceeds 20 and the result would overflow <see cref="long"/>.</exception>
+    public long CalculateFactorial(int n)
+    {
+        if (n < 0)
+            throw new ArgumentOutOfRangeException(nameof(n), "Factorial is not defined for negative numbers.");
+
+        if (n > MaxFactorialInput)
+            throw new OverflowException($"Input {n} is too large; factorial exceeds the range of a 64-bit integer (max supported: {MaxFactorialInput}).");
+
+        long result = 1;
+        for (int i = 2; i <= n; i++)
+        {
+            result *= i;
+        }
+
+        return result;
+    }
+}
diff --git a/api/CourseRegistration.Tests/Services/MathServiceTests.cs b/api/CourseRegistration.Tests/Services/MathServiceTests.cs
new file mode 100644
index 0000000..474e5ce
--- /dev/null
+++ b/api/CourseRegistration.Tests/Services/MathServiceTests.cs
@@ -0,0 +1,75 @@
+using Xunit;
+using CourseRegistration.Application.Services;
+
+namespace CourseRegistration.Tests.Services;
+
+/// <summary>
+/// Unit tests for <see cref="MathService"/> factorial calculation.
+/// </summary>
+public class MathServiceTests
+{
+    private readonly MathService _mathService = new();
+
+    // ── Base cases ─────────────────────────────────────────────────────────────
+
+    [Fact]
+    public void CalculateFactorial_Zero_ReturnsOne()
+    {
+        // Arrange / Act
+        var result = _mathService.CalculateFactorial(0);
+
+        // Assert
+        Assert.Equal(1L, result);
+    }
+
+    [Fact]
+    public void CalculateFactorial_One_ReturnsOne()
+    {
+        // Arrange / Act
+        var result = _mathService.CalculateFactorial(1);
+
+        // Assert
+        Assert.Equal(1L, result);
+    }
+
+    // ── Typical positive values ────────────────────────────────────────────────
+
+    [Theory]
+    [InlineData(2, 2L)]
+    [InlineData(3, 6L)]
+    [InlineData(4, 24L)]
+    [InlineData(5, 120L)]
+    [InlineData(10, 3628800L)]
+    [InlineData(15, 1307674368000L)]
+    [InlineData(20, 2432902008176640000L)]
+    public void CalculateFactorial_PositiveInput_ReturnsCorrectResult(int n, long expected)
+    {
+        // Arrange / Act
+        var result = _mathService.CalculateFactorial(n);
+
+        // Assert
+        Assert.Equal(expected, result);
+    }
+
+    // ── Error paths ────────────────────────────────────────────────────────────
+
+    [Theory]
+    [InlineData(-1)]
+    [InlineData(-100)]
+    [InlineData(int.MinValue)]
+    public void CalculateFactorial_NegativeInputs_ThrowsArgumentOutOfRangeException(int n)
+    {
+        // Arrange / Act / Assert
+        Assert.Throws<ArgumentOutOfRangeException>(() => _mathService.CalculateFactorial(n));
+    }
+
+    [Theory]
+    [InlineData(21)]
+    [InlineData(100)]
+    [InlineData(int.MaxValue)]
+    public void CalculateFactorial_LargeInputs_ThrowsOverflowException(int n)
+    {
+        // Arrange / Act / Assert
+        Assert.Throws<OverflowException>(() => _mathService.CalculateFactorial(n));
+    }
+}