Final answer:
A recursive program to find the factorial of a number can be written in Python by defining a function that calls itself with a decremented number, multiplying the results until reaching a base case.
Step-by-step explanation:
To find the factorial of a number using a recursive approach, you can create a program that calls itself with successively smaller numbers until it reaches the base case. In most programming languages, this involves defining a function that handles the recursion. Here is an example written in Python:
def factorial(n):
if n == 1:
return 1
else:
return n * factorial(n-1)
number = int(input('Enter a number: '))
print('The factorial of', number, 'is', factorial(number))
The factorial function is defined with a base case that returns 1 when the input number is 1. For all other cases, the function calls itself with the argument decreased by one and multiplies the result by the current number, effectively calculating the factorial.