Python program to find the gcd of two numbers

Difficulty Level : Easy
Last Updated : 26 Nov, 2020

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

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

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-

Let a, b be the two numbers
a mod b = R
Let a = b and b = R
Repeat Steps 2 and 3 until a mod b is greater than 0
GCD = b
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

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