Problem Statement: Write a Python program to find factorial of a number using recursion and the loop.

Description: Factorial of a number can be calculated by the following formula.

`n! = n*(n-1)*(n-2)*(n-3)........(3)*(2)*(1)`

Note that that factorial of 1 is 1 and 0 is also 1.

Example:

```
Input: 5
Output: The Factorial of 5 is 120.
Explanation: 5*4*3*2*1 = 120
Input: 7
Output: The Factorial of 7 is 5040.
Explanation: 7*6*5*4*3*2*1 = 5040
```

Enough of theory now lets jump right into coding a Python program to find factorial of a number.

## Python Program: Find Factorial using For loop

This is the easiest approach to find factorial of a number which is easy to understand for beginners. It is a general solution for beginners to use for loop to find factorial of a number.

```
num = int(input("Enter the Number: "))
fact = 1
for i in range(1, num+1):
fact*=i
print(fact)
```

Enter the Number: 5 The factorial of 5 is 120

We take the input and convert to integer type in the first line because by default `input()`

returns string.

The for loop has ranged from 1 to `num`

(inclusive) and we multiply each value to the variable `fact`

. This is same as we described in the formula.

## Python Program: Find factorial using recursion

This is the most popular way to find factorial of a number. In a programming interview, it is often asked to write a Python program to find factorial of a number using recursion.

```
def find_fact(num):
if(num==1):
return 1
return num*find_fact(num-1)
if __name__ == "__main__":
num = int(input("Enter the Number: "))
print("The factorial of {0} is {1}".format(num, find_fact(num)))
```

Enter the Number: 5 The factorial of 5 is 120

Recursion may be a confusing topic for beginners but it is easy to understand.

Here is the image that explains the breakdown of the recursive function.

## Find factorial Using Math module

```
import math
num = int(input("Enter the Number: "))
fact = math.factorial(num)
print("The factorial of {0} is {1}".format(num, fact))
```

Enter the Number: 5 The factorial of 5 is 120

The inbuilt math module in Python is very useful when dealing with mathematical operations. It has some very optimized functions to do various calculations behind the scenes.

The math module also has an inbuilt function to find factorial of a number. The `fact()`

function takes an integer number as argument and returns the factorial of the number.

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