Add Euclidean Algorithm

code/code/mathematical_algorithms/src/euclidean/euclideangcd.py

@@ -0,0 +1,33 @@
+from __future__ import annotations
+from typing import List
+
+def int_division(a:int,b:int)->List:
+    """
+    Implementation of the Division Algorithm
+        -If a,b are elements of the naturals
+        -There exists a unique pair of integers q,r with q>=0 and 0<=r<b
+        -Such that a = (q*b) + r
+    >>> int_division(7,2)
+    [3,2,1]
+    >>> int_division(4,1)
+    [4,1,0]
+    """
+    quotient = a//b
+    remainder = a%b
+    return [quotient,b,remainder]
+
+def euclidean_algorithm(a:int,b:int)->int:
+    """
+    Implementation of the Euclidean Algorithm
+    >>> euclidean_algorithm(4,9)
+    1
+    >>> euclidean_algorithm(23814,8232)
+    294
+    """
+    remainder = int_division(a, b)[2]
+    c = int_division(a, b)[1]
+    quotient = int_division(a, b)[0]
+    if remainder == 0:
+        return c
+    else:
+        return euclidean_algorithm(c, remainder)