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# Python Program to Find Factorial of a Number

Last Updated on April 26, 2023 by Prepbytes Factorial is a fundamental concept in mathematics and computer science. A factorial program in Python calculates the factorial of a given number. In this article, we will understand what is a factorial in python, different approaches of finding factorial along with code and we will also look at some applications of factorial in Python. So, without any further delay, lets move on to our next section.

## What is a Factorial?

Factorial is a mathematical operation denoted by the symbol ! (exclamation mark), used to calculate the product of all positive integers up to a given non-negative integer. For example, the factorial of 5 (denoted by 5!) is calculated as 5 x 4 x 3 x 2 x 1 = 120.

Factorial has several properties, including:

• 0! = 1
• 1! = 1
• n! = n x (n-1)!
• The factorial of a negative integer is undefined (i.e., (-n)! is not defined).
• The factorial function grows very quickly, and for large values of n, it can overflow the capacity of standard data types like integers.

Factorials are used in many programming languages, including Python, to solve various computational problems, including permutations, combinations, and probability distributions.

### Steps in Factorial Program in Python

• Get a positive integer input (n) from the user.
• Iterate from 1 to n using a for loop (for loop is used to increment the number up to the given input)
• Using the below formula, calculate the factorial of a number = f*i.
• Print the output i.e the calculated factorial.

## Different Approaches used to find Factorial of a Number in Python

There are several ways to implement a factorial program in Python. Here are three common approaches:

### Approach 1: Using Factorial Function in Python Factorial Program.

Using the built-in factorial() function is a straightforward approach to implementing the factorial program in Python. Here’s the implementation of the factorial program in Python using the factorial() function.

Code Implementation

```import math

num = 5
factorial = math.factorial(num)

print("The factorial of", num, "is", factorial)```

Output:

``The factorial of 5 is 120``

Explanation: In this program, we first import the math module to gain access to the factorial() function then assign a integer to variable num. We calculate the factorial of num using math.factorial(num).

### Approach 2: Using For Loop in Python Factorial program.

Another approach to implementing the factorial program in Python is by using a for loop. Here’s the implementation of the factorial program in Python using a for loop.

Code Implementation

```n = int (input ("Enter a number: "))
factorial = 1
if n >= 1:
for i in range (1, n+1):
factorial=factorial *i
print("Factorial of the given number is: ", factorial)
```

Output:

``The factorial of 5 is 120``

Explanation: In the above approach, the factorial program takes input from the user as an integer and assigns it to the variable n. It then initializes the variable factorial to 1. If n is greater than or equal to 1, it enters a for loop that iterates from 1 to n (inclusive) and multiplies factorial by each value of i in the loop.

### Approach 3: Using Recursion in Python Factorial program.

Code Implementation

```# Factorial of a number using recursion
def recur_factorial(n):
if n == 1:
return n
else:
return n*recur_factorial(n-1)

num = 5

# 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:
print("The factorial of", num, "is", recur_factorial(num))
```

Output:

``The factorial of 5 is 120``

Explanation: In this factorial program in Python, we define a function recur_factorial that calculates the factorial of a given number n using recursion. If n is 1, the function returns 1, otherwise, it returns n multiplied by recur_factorial(n-1).

### Applications of Factorial in Python

In Python, the factorial has several applications. Some of the applications are:

1. Combinatorics: In combinatorics, factorials are used to calculate the number of possible combinations or permutations of a set of objects.
2. Probability: In probability theory, factorials are used to calculate the number of possible outcomes of a given event.
3. Statistics: In statistics, factorials are used to calculate the number of possible ways to arrange data in a dataset.
4. Cryptography: In cryptography, factorials are used to generate large prime numbers, which are then used in encryption algorithms. Factorial programs can be used to generate these prime numbers.

Conclusion
In this blog, we have discussed the different approaches for finding factorial of a number in Python. We hope this article will help you to clear all your doubts and build your confidence. PrepBytes provides you with the best content also you may check our MYCODE platform to check where you actually stand as these questions are prepared by our expert mentors.

## FAQs

Here are some frequently asked questions on python factorial program.

Q1: What is the difference between iterative and recursive approaches in factorial program in Python?
Ans: In iterative approaches, the factorial of a given number is calculated using a loop that iteratively multiplies the number by its predecessors. In recursive approaches, the factorial is calculated by calling the same function repeatedly until a base case is reached.

Q2: Can a factorial program in Python handle negative numbers?
Ans: No, Factorial program in Python can only handle non-negative integers. Negative numbers do not have factorials.

Q3: Can we calculate the factorial of a decimal number using a factorial program in Python?
Ans: No, we cannot calculate the factorial of a decimal number using a factorial program in Python. Factorials are only defined for non-negative integers.

Q4: What is the time complexity of a recursive factorial program in Python?
Ans: The time complexity of a recursive factorial program in Python is O(n), where n is the input number.

Q5: How can we optimize the performance of factorial program in Python?
Ans: We can optimize the performance of factorial program in Python by using memoization, where we store previously computed factorials to avoid redundant calculations.

Q6: How can we check the performance of a factorial program in Python?
Ans: We can check the performance of a factorial program in Python using the timeit module, which measures the execution time of a given code snippet.