gcd() in Python

The Highest Common Factor (HCF), also called gcd, can be computed in python using a single function offered by math module and hence can make tasks easier in many situations.

Naive Methods to compute gcd

Way 1: Using Recursion

Python3

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

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

a = 60
b = 48

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

Output

The gcd of 60 and 48 is : 12

Way 2: Using Loops

Python3

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

def computeGCD(x, y):

    if x > y:
        small = y
    else:
        small = x
    for i in range(1, small + 1):
        if((x % i == 0) and (y % i == 0)):
            gcd = i

    return gcd

a = 60
b = 48

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

Output

The gcd of 60 and 48 is : 12

Way 3: Using Euclidean Algorithm

Python3

# Python code to demonstrate naive
# method to compute gcd ( Euclidean algo )


def computeGCD(x, y):
    while(y):
       x, y = y, x % y
    return abs(x)

a = 60
b = 48

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

Output:

The gcd of 60 and 48 is : 12

• Both numbers are 0, gcd is 0
• If only either number is Not a number, Type Error is raised.