Question

Implement the function myGCD that recursively used Euclid's algorithm to calculate the greatest common divisor of two numbers. Following is the algorithm:

myGCD(x,y)={x if y = 0
{myGCD(y,remainder(x,y)) if y > 0
Scheme has a built-in remainder function, which you can use for this problem. Also, Scheme already has a built-in ged function, which you shouldn't use.

Answer 1

The myGCD function is a recursive implementation of Euclid's algorithm in Scheme, where it uses the remainder function to find the greatest common divisor of two numbers by reducing the problem size at each recursive step until the second number becomes zero.

Step-by-step explanation:

Implementing the myGCD Function in Scheme

To implement the function myGCD that calculates the greatest common divisor (GCD) of two numbers using recursion, we will use Euclid's algorithm. This algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.

Here is the Scheme code for the recursive function myGCD:

(define (myGCD x y)
(if (= y 0)
x
(myGCD y (remainder x y))))

Explanation of the code:

If y is 0, return x. This is the base case of the recursion.

If y is greater than 0, call myGCD recursively with y and the remainder of x divided by y.

This function will continue to call itself recursively, reducing the size of the numbers at each step, until y becomes 0, at which point the function will return x, which is the GCD of the original two numbers.