# Find Factorial of Number in Python Using Recursion

(Last Updated On: 26/09/2023)

A factorial of a number is the product of all positive integers less than or equal to that number. In mathematics, the factorial of a non-negative integer n is represented as n! For example, the factorial of 5 is 5! = 5 x 4 x 3 x 2 x 1 = 120. In this tutorial, we will learn how to find the factorial of a number in Python using recursion.

### What is Recursion?

Recursion is a technique in computer programming where a function calls itself until it reaches a specific stopping condition. This allows us to solve problems by breaking them down into smaller sub-problems and solving each sub-problem individually.

## Python Program to Find Factorial of Number Using Recursion

```# Find Factorial of Number in Python Using Recursion
def recur_factorial(n):
if n == 1:
return n
else:
return n*recur_factorial(n-1)

# we are taking a number from user as input
# entered value will be converted to int from string
num = int(input("Enter a number: "))

# check if the number is negative
if num < 0:
print("Sorry, factorial does not exist for negative numbers")
elif num == 0:
print("The factorial of 0 is 1")
else:
# number is passed to the recur_factorial() function
print("The factorial of", num, "is", recur_factorial(num))
```

The code given above calculates the factorial of a number in Python using recursion. Here’s how the code works:

1. recur_factorial(n): This function takes an integer n as an argument and calculates the factorial of that number using recursion.
2. if n == 1:: If the number entered by the user is 1, the function returns 1 as the factorial of 1 is 1.
3. else:: If the number is not 1, the function returns n multiplied by the factorial of n-1. This is where the recursion takes place. The function calls itself with the argument n-1, which is one less than the original number until n becomes 1.
4. num = int(input(“Enter a number: “)): This line of code takes input from the user and converts it to an integer.
5. if num < 0:: If the number entered by the user is negative, an error message is displayed stating that the factorial of a negative number does not exist.
6. “elif“ num == 0:: If the number entered by the user is 0, the code displays the message that the factorial of 0 is 1.
7. else:: If the number entered by the user is positive, the function recur_factorial(num) is called and the result is displayed as the factorial of the number.

#### Output:

``````Enter a number: 5
The factorial of 5 is 120
``````

1. Simplicity: Recursion can make the code much simpler and easier to understand, especially for mathematical problems.
2. Reusability: Recursive functions can be used again and again for solving similar problems, which increases code reusability.
3. Abstraction: Recursion allows us to hide the implementation details and work on the abstract level, making the code more abstract and maintainable.

### Limitations of Using Recursion

2. Memory usage: Recursive functions use a lot of memory because each call creates a new stack frame, which consumes memory.
3. Stack overflow: If the recursion goes too deep, it can cause a stack overflow error. This means that the call stack has exceeded its maximum size, and the program terminates.

### Tips for Using Recursion

1. Always have a base case: A base case is a condition that stops the recursion. Without a base case, the recursion will go on forever and cause a stack overflow error.
2. Use the right data structures: Recursion works well with recursive data structures like trees and links lists.
3. Avoid deep recursion: Deep recursion can cause a stack overflow error, so it’s important to keep the recursion depth under control.

### Conclusion

In this tutorial, we learned about finding the factorial of a number in Python using recursion. We saw the advantages and limitations of using recursion, and also learned some tips for using recursion effectively. Recursion is a powerful technique that can simplify code and make it easier to understand, but it’s important to use it correctly to avoid common pitfalls like stack overflow errors.

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