# Euclid's algorithm for finding the gcd of a number

A more interesting example of the use of a while loop is given by this implementation of Euclid's algorithm for finding the greatest common divisor of two numbers, $\mathrm{gcd}(a,b)$:

>>> a, b = 1071, 462
>>> while b:
...    a, b = b, a % b
...
>>> print(a)
21


The loop continues until b divides a exactly; on each iteration, b is set to the remainder of a//b and then a is set to the old value of b. Recall that the integer 0 evaluates as boolean False so while b: is equivalent to while b != 0:.