Python Program to find GCD of Two Numbers

In this article we will show you, How to write a Python program to find GCD of two numbers using While Loop, Functions, and Recursion.

The Greatest Common Divisor (GCD) is also known as Highest Common Factor (HCF), or Greatest Common Factor (GCF), or Highest Common Divisor (HCD), or Greatest Common Measure (GCM).

In Mathematics, the Greatest Common Divisor (GCD) of two or more integers is the largest positive integer that divides a given integer values without remainder. For example, the GCD value of integer 8 and 12 is 4 because, both 8 and 12 are divisible by 1, 2, and 4 (remainder is 0) and the largest positive integer among them is 4.

NOTE: In order to find the GCD or HCF, we have to pass at least one non-zero value.

Python Program to find GCD of Two Numbers Example 1

This python program allows the user to enter two positive integer values. Next, we are using While loop to restrict the I value to not exceed the user specified values.

Within the while loop, we used the If Statement to check whether the remainder of a % i and a % i equals to zero or not. If true, GCD = I otherwise, skip that value.

# Python Program to find GCD of Two Numbers

a = float(input(" Please Enter the First Value a: "))
b = float(input(" Please Enter the Second Value b: "))

i = 1
while(i <= a and i <= b):
    if(a % i == 0 and b % i == 0):
        gcd = i
    i = i + 1
    
print("\n HCF of {0} and {1} = {2}".format(a, b, gcd))

OUTPUT

Python Program to find HCF of Two Numbers Example 2

This is another approach to find the GCD of two number. Here, we are using the Temp variable to find GCD.

# Python Program to find GCD of Two Numbers

num1 = float(input(" Please Enter the First Value  Num1 : "))
num2 = float(input(" Please Enter the Second Value Num2 : "))

a = num1
b = num2

while(num2 != 0):
    temp = num2
    num2 = num1 % num2
    num1 = temp

gcd = num1   
print("\n HCF of {0} and {1} = {2}".format(a, b, gcd))

OUTPUT

Python Program to find GCD of Two Numbers without using Temp

In this program, we are finding the GCD without using Temp variable

# Python Program to find GCD of Two Numbers

num1 = float(input(" Please Enter the First Value  Num1 : "))
num2 = float(input(" Please Enter the Second Value Num2 : "))

a = num1
b = num2

if(num1 == 0):
    print("\n HCF of {0} and {1} = {2}".format(a, b, b))

while(num2 != 0):
    if(num1 > num2):
        num1 = num1 - num2
    else:
        num2 = num2 - num1

gcd = num1   
print("\n HCF of {0} and {1} = {2}".format(a, b, gcd))

OUTPUT

Python Program to find GCD of Two Numbers using Functions

This program is same as above. However, we are separating the logic using Functions

# Python Program to find GCD of Two Numbers

def findgcd(num1, num2):
    if(num1 == 0):
        print("\n HCF of {0} and {1} = {2}".format(a, b, b))

    while(num2 != 0):
        if(num1 > num2):
            num1 = num1 - num2
        else:
            num2 = num2 - num1
    return num1

a = float(input(" Please Enter the First Value a: "))
b = float(input(" Please Enter the Second Value b: "))

gcd = findgcd(a, b)  
print("\n HCF of {0} and {1} = {2}".format(a, b, gcd))

OUTPUT

Python Program to find GCD of Two Numbers using Recursion

It allows user to enter two positive integer values, and calculate the Greatest Common Divisor of those two values by calling findgcd function recursively.

# Python Program to find GCD of Two Numbers

def findgcd(a, b):
    if(b == 0):
        return a;
    else:
        return findgcd(b, a % b)
    
num1 = float(input(" Please Enter the First Value  Num1 : "))
num2 = float(input(" Please Enter the Second Value Num2 : "))

gcd = findgcd(num1, num2)
print("\n GCD of {0} and {1} = {2}".format(num1, num2, gcd))

OUTPUT