diff --git a/src/arithmetic/arithmetic.py b/src/arithmetic/arithmetic.py
index 86f6960..7a8787f 100644
--- a/src/arithmetic/arithmetic.py
+++ b/src/arithmetic/arithmetic.py
@@ -13,7 +13,7 @@ def add_numbers(a: int, b: int) -> int:
     Returns:
         Sum of a and b.
     """
-    raise NotImplementedError
+    return a + b
 
 
 def factorial(n: int) -> int:
@@ -28,7 +28,12 @@ def factorial(n: int) -> int:
     Raises:
         ValueError: if n is negative
     """
-    raise NotImplementedError
+    if n < 0:
+        raise ValueError("n must be non-negative")
+    result = 1
+    for i in range(2, n + 1):
+        result *= i
+    return result
 
 
 def is_prime(n: int) -> bool:
@@ -43,4 +48,13 @@ def is_prime(n: int) -> bool:
     Returns:
         True if n is prime; otherwise False.
     """
-    raise NotImplementedError
+    if n <= 1:
+        return False
+    if n == 2:
+        return True
+    if n % 2 == 0:
+        return False
+    for i in range(3, int(n ** 0.5) + 1, 2):
+        if n % i == 0:
+            return False
+    return True