maths.greatest_common_divisor
=============================

.. py:module:: maths.greatest_common_divisor

.. autoapi-nested-parse::

   Greatest Common Divisor.

   Wikipedia reference: https://en.wikipedia.org/wiki/Greatest_common_divisor

   gcd(a, b) = gcd(a, -b) = gcd(-a, b) = gcd(-a, -b) by definition of divisibility



Functions
---------

.. autoapisummary::

   maths.greatest_common_divisor.gcd_by_iterative
   maths.greatest_common_divisor.greatest_common_divisor
   maths.greatest_common_divisor.main


Module Contents
---------------

.. py:function:: gcd_by_iterative(x: int, y: int) -> int

   Below method is more memory efficient because it does not create additional
   stack frames for recursive functions calls (as done in the above method).
   >>> gcd_by_iterative(24, 40)
   8
   >>> greatest_common_divisor(24, 40) == gcd_by_iterative(24, 40)
   True
   >>> gcd_by_iterative(-3, -9)
   3
   >>> gcd_by_iterative(3, -9)
   3
   >>> gcd_by_iterative(1, -800)
   1
   >>> gcd_by_iterative(11, 37)
   1


.. py:function:: greatest_common_divisor(a: int, b: int) -> int

   Calculate Greatest Common Divisor (GCD).
   >>> greatest_common_divisor(24, 40)
   8
   >>> greatest_common_divisor(1, 1)
   1
   >>> greatest_common_divisor(1, 800)
   1
   >>> greatest_common_divisor(11, 37)
   1
   >>> greatest_common_divisor(3, 5)
   1
   >>> greatest_common_divisor(16, 4)
   4
   >>> greatest_common_divisor(-3, 9)
   3
   >>> greatest_common_divisor(9, -3)
   3
   >>> greatest_common_divisor(3, -9)
   3
   >>> greatest_common_divisor(-3, -9)
   3


.. py:function:: main()

   Call Greatest Common Divisor function.