This article will explain two different ways to find factorial of a number in python using `for` loop and recursion with explanation and example output.

What is factorial
Factorial of an integer(or a natural number) is the product of all numbers starting from the integer till 1. Example, factorial of 5 will be 5 * 4 * 3 * 2 * 1 = 120.
Thus, factorial of a number n will be n * (n-1) * (n-2) ….. * 1.

Find factorial of a number in python
There are a couple of approaches to find factorial of a number using python. This post will discuss both these approaches.

Method 1: Using for loop
This method finds the factorial of a number by iterating in reverse direction starting from the number till 1 and finding the product in every iteration.
Algorithm for this method comprises of the following steps.

1. Initialize a variable to hold the factorial of number to 1.
2. Loop from the number till 1 with an interval of 1.
3. In every iteration, find the product of number and the variable initialized in step 1 and store it in the same variable
4. After loop completes(when the last number is 1) the variable will be holding the product of all numbers till 1 which is the factorial of the given number.

Factorial program in python written as per the above algorithm is given below.

```# function to calculate factorial of the given number
def fact(number):
# initialize variable to store factorial
fact = 1
# loop from the number till 1
for number in range(5, 1,-1):
# multiply current number with the product of previous numbers
fact = fact * number
return fact

# read number from keyboard
number = int(input("Enter a number\n"))
# find factorial
factorial = fact(number)
print("Factorial is "+str(factorial))```

Explanation
Above code defines a function to calculate factorial of a number. The function initializes a variable to store the factorial and reverse iterates from the number till 1 using a `for` loop and `range` function.

`range` function takes 3 arguments, first is the start value which will be the number itself, second argument is the end number till which you want the loop to execute.

This value will be 1 and third argument is the step value with which we want to iterate. Since we want to reverse iterate by 1 every time, this value will be -1.

In every iteration, we multiply the current value with the value stored in the variable.

Thus, in every iteration, this variable will hold the product of a number with all numbers before it and at the end of the loop it will have the product of all numbers till 1.

Number whose factorial needs to be calculated is read as input from the keyboard using `input` function. Since this function returns the value in string format, we need to convert it to an integer using int function.

Output
Above program produces following output

Enter a number
5
Factorial is 120

Using while loop
It is also possible to use `while` loop in place of `for` loop in this method with a slight modification.

Loop will continue till the number is greater than equal to 1 and in each iteration, the number is decreased by 1 inside the loop as shown below.

```def fact_while(number):
# initialize variable to hold factorial
fact = 1
# loop till the number reaches 1
while number >= 1:
# multiply current number with the product of previous numbers
fact = fact * number
# reduce the number by 1
number = number - 1
return fact
```

Output remains the same.

Method 2: Using recursion
Recursion means a method calling itself till some condition is met. A method which calls itself is called a recursive method.
A recursive method should have a condition which must cause it to return else it will keep on calling itself infinitely resulting in memory over flow.
Calculating the factorial of a number using recursive method should work on the following algorithm.

1. Create a method which accepts one argument.
2. Check if the value of argument is 1, then return 1 from this method. This will be the terminating condition of the recursive method.
3. Return the product of the argument and the return value of this method called with (argument – 1).

Code follows

```# recursive method which returns the factorial of a number
def factorial_recursion(number):
# check if number is 1
if number == 1:
# return 1 from the method
return 1
return number * factorial_recursion(number-1)

# factorial = factorial_recursion(5)
# read number from keyboard
number = int(input("Enter a number\n"))
# find factorial
factorial = fact(number)
print("Factorial is "+str(factorial))
```

The method will keep on calling itself and return the product of argument supplied to it with 1 less than the argument. When the argument value is 1, it will return 1.
This way, the recursive method will return the product of all the numbers starting from the argument till 1.

Output
Output of the above program will be

Enter a number
5
Factorial is 120

Hope this article helped you to understand the logic to find the factorial of a number in python using a loop and recursive function.

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