Question

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:

```python
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`.