Code for Greatest Common Divisor in Python [closed]

The greatest common divisor (GCD) of a and b is the largest number that divides both of them with no remainder.

One way to find the GCD of two numbers is Euclid’s algorithm, which is based on the observation that if r is the remainder when a is divided by b, then gcd(a, b) = gcd(b, r). As a base case, we can use gcd(a, 0) = a.

Write a function called gcd that takes parameters a and b and returns their greatest common divisor.

Solution 1:

It's in the standard library.

>>> from fractions import gcd
>>> gcd(20,8)
4

Source code from the inspect module in Python 2.7:

>>> print inspect.getsource(gcd)
def gcd(a, b):
    """Calculate the Greatest Common Divisor of a and b.

    Unless b==0, the result will have the same sign as b (so that when
    b is divided by it, the result comes out positive).
    """
    while b:
        a, b = b, a%b
    return a

As of Python 3.5, gcd is in the math module; the one in fractions is deprecated. Moreover, inspect.getsource no longer returns explanatory source code for either method.

Solution 2:

The algorithms with m-n can runs awfully long.

This one performs much better:

def gcd(x, y):
    while y != 0:
        (x, y) = (y, x % y)
    return x

Solution 3:

This version of code utilizes Euclid's Algorithm for finding GCD.

def gcd_recursive(a, b):
    if b == 0:
        return a
    else:
        return gcd_recursive(b, a % b)

Solution 4:

gcd = lambda m,n: m if not n else gcd(n,m%n)

Solution 5:

using recursion,

def gcd(a,b):
    return a if not b else gcd(b, a%b)

using while,

def gcd(a,b):
  while b:
    a,b = b, a%b
  return a

using lambda,

gcd = lambda a,b : a if not b else gcd(b, a%b)

>>> gcd(10,20)
>>> 10