Question

write a racket function that determines the greatest common divisor of two positive integer numbers. you must use the lambda function definition for this question.

Answer 1

A Racket function can be written using lambda expressions to calculate the greatest common divisor of two integers based on the Euclidean algorithm, applying recursion for this calculation.

Step-by-step explanation:

We can write a racket function using lambda expressions to compute the greatest common divisor (GCD) of two positive integer numbers. The Euclidean algorithm is a classical method to obtain the GCD. Using recursive lambda, we can define the GCD function as follows:

(define gcd
(lambda (a b)
(if (= b 0)
a
((lambda (a b) (gcd b (modulo a b))) a b))))

This function works by checking if the second argument b is zero. If it is, it returns the first argument a as the GCD. If not, it applies the lambda recursively with the new parameters b and a mod b.