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?

(1 point)
Responses

def factorial(n):
if n == 0:
return 1
else:
if n % 2 == 0:
return n * factorial(n - 2)
else:
return factorial(n - 1)
print("The answer is", factorial(7))
def factorial(n): if n == 0: return 1 else: if n % 2 == 0: return n * factorial(n - 2) else: return factorial(n - 1) print("The answer is", factorial(7))

def factorial(n):
if n == 1:
return n
else:
return n * factorial(n - 2)
print("The answer is", factorial(7))
def factorial(n): if n == 1: return n else: return n * factorial(n - 2) print("The answer is", factorial(7))

def factorial(n):
if n <= 1:
return n
else:
return n * factorial(n - 2)
print("The answer is", factorial(7))
def factorial(n): if n <= 1: return n else: return n * factorial(n - 2) print("The answer is", factorial(7))

def factorial(n):
if n <= 1:
return 1
else:
if n % 2 != 0:
return n * factorial(n - 2)
else:
return factorial(n - 1)
print("The answer is", factorial(7))

Answer 1

To modify the given program to compute the product of all even numbers less than 7, we need to ensure we only consider even numbers and correctly handle the base case of the recursion.

Out of the provided options, here’s the correct one:

```python
def factorial(n):
if n == 0:
return 1
else:
if n % 2 == 0:
return n * factorial(n - 2)
else:
return factorial(n - 1)
print("The answer is", factorial(7))
```

### Explanation:
1. The base case is defined for `n == 0` to return 1, which is appropriate because the product of an empty set (or even the product of numbers up to zero) is 1.
2. The recursive part of the function checks if `n` is even (`n % 2 == 0`). If it is, it multiplies `n` with the factorial of `n - 2`, thus only counting even numbers.
3. If `n` is odd, it simply calls the function with `n - 1`, thus skipping the odd number and moving to the next lower even number.

Therefore, this function will calculate `6 * 4 * 2`, which covers all even numbers less than 7. The answer printed would be the product of these even numbers.