Python Program to Find the Factorial of a Number

What’s Factorial?

In easy phrases, if you wish to discover the factorial of a optimistic integer, maintain multiplying it with all of the optimistic integers lower than that quantity. The ultimate end result that you simply get is the factorial of that quantity. So if you wish to discover the factorial of seven, multiply 7 with all optimistic integers lower than 7, and people numbers can be 6,5,4,3,2,1. Multiply all these numbers by 7, and the ultimate result’s the factorial of seven.

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Formulation of Factorial

Factorial of a quantity is denoted by n! is the product of all optimistic integers lower than or equal to n:
n! = n*(n-1)*(n-2)*…..3*2*1

10 Factorial

So what’s 10!? Multiply 10 with all of the optimistic integers that are lower than 10.
10! =10*9*8*7*6*5*4*3*2*1=3628800

Factorial of 5

To seek out ‘5!’ once more, do the identical course of. Multiply 5 with all of the optimistic integers lower than 5. These numbers can be 4,3,2,1
5!=5*4*3*2*1=120

Factorial of 0

Since 0 just isn’t a optimistic integer, as per conference, the factorial of 0 is outlined to be itself.
0!=1

Computing that is an attention-grabbing downside. Allow us to take into consideration why easy multiplication can be problematic for a pc. The reply to this lies in how the answer is applied.

1! = 1
2! = 2
5! = 120
10! = 3628800
20! = 2432902008176640000
30! = 9.332621544394418e+157

The exponential rise within the values exhibits us that factorial is an exponential perform, and the time taken to compute it could take exponential time.

Factorial Program in Python

We’re going to undergo 3 methods wherein we are able to calculate factorial:

• Utilizing a perform from the maths module
• Iterative strategy(Utilizing for loop)
• Recursive strategy

import math
num=int(enter("Enter the quantity: "))
print("factorial of ",num," (perform): ",finish="")
print(math.factorial(num))

def iter_factorial(n):
    factorial=1
    n = enter("Enter a quantity: ")
    factorial = 1
    if int(n) >= 1:
        for i in vary (1,int(n)+1):
            factorial = factorial * i
        return factorial
  
num=int(enter("Enter the quantity: "))

print("factorial of ",num," (iterative): ",finish="")
print(iter_factorial(num))

TEST THE CODE

Enter – Enter the quantity: 5
Output – Factorial of 5 (iterative) : 120

Think about the iterative program. It takes a number of time for the whereas loop to execute. The above program takes a number of time, let’s say infinite. The very objective of calculating factorial is to get the end in time; therefore, this strategy doesn’t work for big numbers.

Factorial program in Python utilizing recursion

def recur_factorial(n):
    """Perform to return the factorial
    of a quantity utilizing recursion"""
    if n == 1:
        return n
    else:
        return n*recur_factorial(n-1)

num=int(enter("Enter the quantity: "))

print("factorial of ",num," (recursive): ",finish="")
print(recur_factorial(num))

TEST THE CODE

Enter – Enter – Enter the quantity : 4
Output – Factorial of 5 (recursive) : 24

On a 16GB RAM pc, the above program may compute factorial values as much as 2956. Past that, it exceeds the reminiscence and thus fails. The time taken is much less when in comparison with the iterative strategy. However this comes at the price of the house occupied.

What’s the resolution to the above downside?
The issue of computing factorial has a extremely repetitive construction.

To compute factorial (4), we compute f(3) as soon as, f(2) twice, and f(1) thrice; because the quantity will increase, the repetitions enhance. Therefore, the answer can be to compute the worth as soon as and retailer it in an array from the place it may be accessed the following time it’s required. Subsequently, we use dynamic programming in such instances. The situations for implementing dynamic programming are

1. Overlapping sub-problems
2. optimum substructure 

Think about the modification to the above code as follows:

def DPfact(N):
    arr={}
    if N in arr:
        return arr[N]
    elif N == 0 or N == 1:
        return 1
        arr[N] = 1
    else:
        factorial = N*DPfact(N - 1)
        arr[N] = factorial
    return factorial
    
num=int(enter("Enter the quantity: "))

print("factorial of ",num," (dynamic): ",finish="")
print(DPfact(num))

TEST THE CODE

Enter – Enter the quantity: 6
Output – factorial of 6 (dynamic) : 720

A dynamic programming resolution is very environment friendly by way of time and house complexities.

Rely Trailing Zeroes in Factorial utilizing Python

Drawback Assertion: Rely the variety of zeroes within the factorial of a quantity utilizing Python

num=int(enter("Enter the quantity: "))
  
# Initialize end result 
rely = 0
# Hold dividing n by 
# powers of 5 and 
# replace Rely 
temp = 5
whereas (num / temp>= 1):
    rely += int(num / temp) 
    temp *= 5

# Driver program  
print("Variety of trailing zeros", rely)

Output
Enter the Quantity: 5
Variety of trailing zeros 1

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