Q$\mathrm{.}1)(20)$ In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor $($GCD$)$ of two integers, the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements $($c$.300BC).$ It is an example of an algorithm, a step$-$by$-$step procedure for performing a calculation according to well$-$defined rules, and is one of the oldest algorithms in common use. It can reduce fractions to their simplest form and is a part of many other number$-$theoretic and cryptographic calculations.

For illustration, the Euclidean algorithm can find the greatest common divisor of $a=1071$ and $b=462$ :

$1071-462$

$609-462$

$147-462$

$147-315$

$147-168$

$147-21$

$126-21$

$105-21$

$84-21$

$63-21$

$42-21$

$21-21$

Provide an iterative implementation of GCD using only subtraction in Python: