# Python Program to find GCD of Two Numbers

Write a Python program to find the GCD of two numbers using While Loop, Functions, and Recursion. To find the GCD or HCF, we have to pass at least one non-zero value.

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

## 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 the While loop to restrict the i value not to exceed the user-specified values.

Within the While loop, we used the If Statement to check whether a%i and a % i remainder equal to zero or not. If true, Highest Common Factor = I otherwise skip that value.

```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):
val = i
i = i + 1

print("\n HCF of {0} and {1} = {2}".format(a, b, val))```
`````` Please Enter the First Value a: 8
Please Enter the Second Value b: 12

HCF of 8.0 and 12.0 = 4``````

## Python Program to find HCF of Two Numbers Example 2

It is another approach to finding the Greatest Common Factor of two numbers. In this program, we are using the Temp variable to find GCD.

```num1 = float(input(" First : "))
num2 = float(input(" Second : "))

a = num1
b = num2

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

hcf = num1
print("\n HCF of {0} and {1} = {2}".format(a, b, hcf))```
`````` First : 12
Second : 36

HCF of 12.0 and 36.0 = 12.0``````

## Without using Temp

In this Python program, we are finding the GCD of two numbers without using the Temp variable.

```num1 = float(input(" First : "))
num2 = float(input(" Second : "))

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

hcf = num1
print(hcf)```
`````` First : 75
Second : 255

HCF of 75.0 and 255.0 = 15.0``````

## Python Program to find GCD of Two Numbers using Functions

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

```def findresult(val1, val2):
if(val1 == 0):
print("\n HCF of {0} and {1} = {2}".format(a, b, b))

while(val2 != 0):
if(val1 > val2):
val1 = val1 - val2
else:
val2 = val2 - val1
return val1

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

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

## GCD of Two Numbers using Recursion

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

```def findGreatestCD(a, b):
if(b == 0):
return a;
else:
return findGreatestCD(b, a % b)

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

Val = findGreatestCD(num1, num2)
print("\n The Result of {0} and {1} = {2}".format(num1, num2, Val))```
`````` Please Enter the First Value  : 22
Please Enter the Second Value : 88

The Result of 22.0 and 88.0 = 22.0``````