Python Program for Basic Euclidean algorithms

Last Updated : 23 Jul, 2025

Python3

# Python program to demonstrate Basic Euclidean Algorithm 


# Function to return gcd of a and b 
def gcd(a, b): 
    if a == 0 : 
        return b 
    
    return gcd(b%a, a) 

a = 10
b = 15
print("gcd(", a , "," , b, ") = ", gcd(a, b)) 

a = 35
b = 10
print("gcd(", a , "," , b, ") = ", gcd(a, b)) 

a = 31
b = 2
print("gcd(", a , "," , b, ") = ", gcd(a, b)) 

# Code Contributed By Mohit Gupta_OMG <(0_o)>

Output:

GCD(10, 15) = 5
GCD(35, 10) = 5
GCD(31, 2) = 1

Time Complexity: O(Log min(a, b))

Auxiliary Space: O(Log min(a, b)), due to recursion stack.

Please refer complete article on Basic and Extended Euclidean algorithms for more details!

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