maths.reverse_factorial_recursive
=================================

.. py:module:: maths.reverse_factorial_recursive


Functions
---------

.. autoapisummary::

   maths.reverse_factorial_recursive.reverse_factorial_recursive


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

.. py:function:: reverse_factorial_recursive(value: int, current_divisor: int = 1) -> int

   Return x such that x! == value, otherwise return -1.

   The function divides `value` by 1, 2, 3, ... recursively. If the repeated
   division reduces `value` exactly to 1, the factorial root x is
   (current_divisor - 1). If the division ever has a remainder, no integer x
   exists and the function returns -1.

   Parameters
   ----------
   value: The positive integer to test (candidate factorial value).
   current_divisor: The current divisor used while reducing `value` (default is 1).

   Returns
   -------
   The factorial root (x) if x! == value, otherwise -1.

   Examples
   --------
   >>> reverse_factorial_recursive(120)
   5
   >>> reverse_factorial_recursive(24)
   4
   >>> reverse_factorial_recursive(150)
   -1
   >>> reverse_factorial_recursive(1)
   1
   >>> reverse_factorial_recursive(2)
   2