Python program to find the gcd of two numbers

Given two numbers. The task is to find the GCD of the two numbers.

Using STL :

In Python, the math module contains a number of mathematical operations, which can be performed with ease using the module. math.gcd() function compute the greatest common divisor of 2 numbers mentioned in its arguments.

Syntax: math.gcd(x, y)

Parameter:

x : Non-negative integer whose gcd has to be computed.

y : Non-negative integer whose gcd has to be computed.

Returns: An absolute/positive integer value after calculating the GCD of given parameters x and y. Exceptions: When Both x and y are 0, function returns 0, If any number is a character, Type error is raised.

Python3

# Python code to demonstrate the working of gcd()
# importing "math" for mathematical operations
import math

# prints 12
print("The gcd of 60 and 48 is : ", end="")
print(math.gcd(60, 48))

Output

The gcd of 60 and 48 is : 12

Time complexity:  O(log(min(a,b))), as it uses the Euclidean Algorithm for finding the GCD.
Auxiliary Space: O(log(n)), as it uses recursion and the maximum depth of recursion is log(n).

Using Recursion :

Python3

# Python code to demonstrate naive
# method to compute gcd ( recursion )


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

a = 60
b = 48

# prints 12
print("The gcd of 60 and 48 is : ", end="")
print(hcf(60, 48))

Output

The gcd of 60 and 48 is : 12

Time complexity:  O(log(min(a,b))), as it uses the Euclidean Algorithm for finding the GCD.
Auxiliary Space: O(log(n)), as it uses recursion and the maximum depth of recursion is log(n).

Using Euclidean Algorithm :

The Euclid’s algorithm (or Euclidean Algorithm) is a method for efficiently finding the greatest common divisor (GCD) of two numbers. The GCD of two integers X and Y is the largest number that divides both of X and Y (without leaving a remainder).

Pseudo Code of the Algorithm-

1. Let  a, b  be the two numbers
2. a mod b = R
3. Let  a = b  and  b = R
4. Repeat Steps 2 and 3 until  a mod b  is greater than 0
5. GCD = b
6.  Finish

Python3

# Recursive function to return gcd of a and b
def gcd(a, b):

    # Everything divides 0
    if (a == 0):
        return b
    if (b == 0):
        return a

    # base case
    if (a == b):
        return a

    # a is greater
    if (a > b):
        return gcd(a-b, b)
    return gcd(a, b-a)

# Driver program to test above function
a = 98
b = 56
if(gcd(a, b)):
    print('GCD of', a, 'and', b, 'is', gcd(a, b))
else:
    print('not found')

Output

GCD of 98 and 56 is 14

Time complexity: O(log(min(a,b))), as it uses the Euclidean algorithm which has a time complexity of O(log(min(a,b))). 
Auxiliary Space: O(1), as it only uses a few variables and does not require any additional data structures.