Consider the recursive function for the calculation of a factorial. def factorial(n): if n == 1: return n else: return n * factorial(n - 1) print("The factorial of", 7, "is", factorial(7)) How could the program be modified to print the product of all the even numbers less than 7?

Answer 1

You can modify the provided recursive function to calculate the product of all even numbers less than a given threshold instead of calculating the factorial. Here's how you can implement this:

def product_of_evens(n):
    if n <= 2:  # Base case: if n is 2 or less, there are no even numbers less than n to multiply
        return 1  # Return 1 because multiplying by 1 doesn't affect the product
    elif n % 2 == 0:  # If n is even, include n-2 in the product
        return (n - 2) * product_of_evens(n - 2)
    else:  # If n is odd, start from the next lower even number
        return (n - 1) * product_of_evens(n - 1)

print("The product of all even numbers less than 7 is", product_of_evens(7))

Explanation:

1. Base Case: The function product_of_evens checks if n is less than or equal to 2. If so, it returns 1 because there are no even numbers less than 2.
2. Even Case: If n is even, the function multiplies n - 2 (the next even number less than n) by the result of the function called recursively with n - 2.
3. Odd Case: If n is odd, it multiplies n - 1 by the result of the function called recursively with n - 1 to handle the nearest even number.

This way, the function will multiply all even numbers less than the input n. For the input of 7, the even numbers less than 7 are 2, 4, and 6, and the final result will be 2 * 4 * 6 = 48.