Last Updated on June 5, 2023 by Mayank Dham

The factorial of a non-negative integer is a mathematical operation that calculates the product of all positive integers less than or equal to that number. It is denoted by the exclamation mark (!) after the number. For example, the factorial of 5 is written as 5!, and it is calculated as 5 × 4 × 3 × 2 × 1 = 120. Factorials are commonly used in mathematics, statistics, and various computational algorithms. They are often used to solve problems involving permutations, combinations, and counting arrangements.

Factorial number in Python using Recursion

Finding the factorial of a number using recursion involves defining a function that calls itself with smaller inputs until it reaches a base case. The factorial of a number is calculated by multiplying that number with the factorial of its preceding positive integers.

Here’s a brief introduction to finding the factorial of a number using recursion:

Step 1: Define a recursive function called factorial that takes an integer n as an input.

Step 2: Set up a base case: If n is 0 or 1, return 1 since the factorial of 0 or 1 is 1.

Step 3: In the recursive case, call the factorial function with n-1 as the argument and multiply the result by n.

Step 4: Return the result obtained from the recursive call.

Step 5: To find the factorial of a specific number, invoke the factorial function with the desired number as an argument.

Recursion is a technique where a function solves a problem by dividing it into smaller subproblems of the same type. By repeatedly solving these smaller subproblems and combining their results, the solution to the original problem is obtained.

## Implementation

```
def factorial(n):
if n == 0 or n == 1:
return 1
else:
return n * factorial(n - 1)
print(factorial(5))
```

**Output**

`120`

**Conclusion**

In conclusion, finding the factorial of a number using recursion involves defining a function that calls itself with smaller inputs until it reaches a base case. Recursion allows us to break down the problem into smaller subproblems and solve them iteratively. By applying the recursive approach, the factorial of a number can be calculated by multiplying that number with the factorial of its preceding positive integers.

Recursion provides an elegant and concise solution to compute factorials. However, it’s important to consider the efficiency of recursive algorithms, as they may have higher time and space complexity compared to iterative approaches for large inputs.

Overall, the recursive approach to finding the factorial of a number is a fundamental example of using recursion to solve mathematical problems, and it demonstrates the power of breaking down complex tasks into simpler, self-referential steps.

## Frequently Asked Questions

**Q1. What is the base case in the recursive factorial function?**

The base case in the recursive factorial function is when the input number n is 0 or 1. In this case, the function returns 1 since the factorial of 0 or 1 is defined as 1.

**Q2. Can the factorial function handle negative numbers?**

No, the factorial function using recursion is typically defined for non-negative integers. It is not defined for negative numbers as factorial is not defined for them.

**Q3. Are there any limitations to using recursion for calculating factorials?**

Yes, using recursion to calculate factorials has limitations. Recursion has a performance impact when dealing with large numbers due to the stack space used for recursive function calls. It can lead to stack overflow errors for very large inputs.

**Q4. How does the recursive factorial function work?**

The recursive factorial function works by breaking down the problem into smaller subproblems. It calls itself with a smaller input (n-1) until it reaches the base case. The function multiplies the current number n with the result of the factorial of the smaller input (n-1), and this process continues until the base case is reached and the recursion stops.

**Q5. Can the factorial function be implemented iteratively instead of recursively?**

Yes, the factorial function can be implemented iteratively using loops instead of recursion. It is often more efficient in terms of performance and stack space utilization, especially for larger inputs.

**Q6. Is there a limit to the input size that can be used with the recursive factorial function?**

The limit to the input size of the recursive factorial function depends on the maximum stack space available for function calls. For very large inputs, it may exceed the available stack space and result in stack overflow errors. In such cases, an iterative approach or a more optimized algorithm is preferred.