Program to input two numbers as input and compute the greatest common divisor

Write a program to input two numbers as input and compute the greatest common divisor.

def gcd(x, y):
    gcd = 1
    if x % y == 0:
        return y
    for k in range(int(y / 2), 0, -1):
        if x % k == 0 and y % k == 0:
            gcd = k
            break
    return gcd

n1 = int(input('n1: '))
n2 = int(input('n2: '))
print("GCD of", n1, '&', n2, 'is', gcd(n1, n2))

Output : 
n1: 48
n2: 18
GCD of 48 & 18 is 6

Certainly! The provided Python code defines a function gcd that calculates the greatest common divisor (GCD) of two numbers using a loop and the Euclidean algorithm. The code also prompts the user to input two numbers and then prints their GCD. Here’s a detailed explanation of how the code works:

Explanation

1. Function Definition (def gcd(x, y):):

• This line defines a function named gcd that takes two parameters, x and y, which are the two numbers whose GCD needs to be calculated.

1. Check if y Divides x Exactly (if x % y == 0:):

• This line checks if y is a divisor of x. If x modulo y is 0, then y is the GCD, and the function returns y.

1. Loop to Find GCD:

   for k in range(int(y / 2), 0, -1):
       if x % k == 0 and y % k == 0:
           gcd = k
           break

• If y does not divide x exactly, the function enters a for loop.
• The loop starts from int(y / 2) and goes down to 1. It checks each number k to see if it is a common divisor of both x and y.
• The first common divisor found (x % k == 0 and y % k == 0) is stored in gcd, and the loop breaks immediately.

1. Return GCD:

   return gcd

• The function returns the value of gcd, which is the greatest common divisor found by the loop.

1. Input and Function Call:

• The user is prompted to input two numbers:
  python n1 = int(input('n1:')) n2 = int(input('n2:'))
• These inputs are stored in variables n1 and n2.
• The gcd function is called with n1 and n2 as arguments, and the result is printed:
  python print("GCD of", n1, '&', n2, 'is', gcd(n1, n2))

Example

Let’s go through an example where the user inputs two numbers. Suppose the user inputs the following:

n1: 48
n2: 18

The code execution will be as follows:

• Input Numbers:

  n1 = 48
  n2 = 18

• Function Call:

  gcd(48, 18)

• Check if 18 Divides 48:
• 48 % 18 is not 0, so the function proceeds to the loop.
• Loop to Find GCD:
• The loop starts at int(18 / 2) = 9 and checks down to 1:
  • For k = 9: 48 % 9 != 0
  • For k = 8: 48 % 8 != 0
  • For k = 7: 48 % 7 != 0
  • For k = 6: 48 % 6 == 0 and 18 % 6 == 0, so gcd = 6 and the loop breaks.
• Return and Print Result:

  GCD of 48 & 18 is 6

Summary

This code defines a function gcd to calculate the greatest common divisor of two numbers. It first checks if one number exactly divides the other. If not, it uses a loop to find the highest common divisor by checking divisors from half of the smaller number down to 1. The user is prompted to input two numbers, and the GCD of these numbers is printed.