Question

Write a program that can do the following tasks:

1) input two integer numbers from the keyboard.
2) compute the greatest common divisor (gcd) of these two integers using the Euclidean algorithm as described in the equation below. Note that remainder (x,y) can be evaluated using the modulo operator %.

Answer 1

To compute the gcd of two integers using the Euclidean algorithm, prompt the user to enter the numbers, calculate the gcd using the algorithm, and output the result.

Step-by-step explanation:

To write a program that can compute the greatest common divisor (gcd) using the Euclidean algorithm, you can follow these steps:

1. First, prompt the user to enter two integer numbers from the keyboard.
2. Next, calculate the gcd using the Euclidean algorithm. The algorithm proceeds as follows:

• Set variables 'a' and 'b' to the two input numbers respectively.
• While 'b' is not equal to 0, calculate the remainder of 'a' divided by 'b' using the modulo operator (%).
• Set 'a' to the value of 'b' and 'b' to the remainder.

Finally, output the computed gcd.

Here's an example Python code:

a = int(input('Enter the first number: '))
b = int(input('Enter the second number: '))

while b != 0:
remainder = a % b
a = b
b = remainder

print('The gcd is:', a)