diff --git a/maths/factorial_iterative.py b/maths/factorial_iterative.py
new file mode 100644
index 000000000000..752f355b8821
--- /dev/null
+++ b/maths/factorial_iterative.py
@@ -0,0 +1,23 @@
+def factorial_iterative(number: int) -> int:
+    """
+    Return the factorial of a non-negative integer using an iterative method.
+
+    >>> factorial_iterative(5)
+    120
+    >>> factorial_iterative(0)
+    1
+    >>> factorial_iterative(1)
+    1
+    """
+    if number < 0:
+        raise ValueError("Input must be a non-negative integer")
+
+    result = 1
+    for i in range(2, number + 1):
+        result *= i
+    return result
+
+
+if __name__ == "__main__":
+    # simple demonstration
+    print(factorial_iterative(5))  # expected 120
diff --git a/maths/gcd_iterative.py b/maths/gcd_iterative.py
new file mode 100644
index 000000000000..3d3cd7d4ab8b
--- /dev/null
+++ b/maths/gcd_iterative.py
@@ -0,0 +1,13 @@
+def gcd_iterative(first_number: int, second_number: int) -> int:
+    """
+    Compute the greatest common divisor (GCD) of two numbers iteratively.
+
+    Examples:
+    >>> gcd_iterative(48, 18)
+    6
+    >>> gcd_iterative(7, 5)
+    1
+    """
+    while second_number != 0:
+        first_number, second_number = second_number, first_number % second_number
+    return first_number