Strong Number in Python

Strong Number in Python

Introduction

In this tutorial, we will learn how to determine whether a given number is a Strong Number using Python. A strong number is a unique kind of number in which the total of its digits’ factorials equals the number.

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What is a Strong Number?

When the sum of the factorials of a number’s digits equals the number itself, the number is said to be strong.

Example:

Consider the number 145:

• 1! = 1
• 4! = 24
• 5! = 120
• Sum of factorials: 1 + 24 + 120 = 145

145 is a strong number since the sum equals the initial value.

Problem Approach

To determine whether a given number is a Strong Number, follow these steps:

1. Request that the user enter a number.
2. Extract each digit from the number.
3. Compute the factorial of each digit.
4. Sum up all the factorials.
5. Verify that the total equals the initial amount.
6. Print the result.

Sample Input and Output

Input:

num = 132

Output:

Given number is not a strong number.

Input:

num = 145

Output:

Given number is a strong number.

Python Program to Find Strong Number

Let’s implement the logic using a while loop.

Example 1: Using While Loop

# A program that determines whether a given number is a strong number

sum = 0  
num = int(input("Enter a number: "))  
temp = num  

while num > 0:  
    i = 1  
    fact = 1  
    rem = num % 10  
    
    while i <= rem:  
        fact *= i   # Compute factorial  
        i += 1  
    
    sum += fact  
    num //= 10  

if sum == temp:  
    print("Given number is a Strong Number")  
else:  
    print("Given number is not a Strong Number")  

Output:

Enter a number: 145
Given number is a Strong Number.

Explanation of the Code

1. The user inputs a number.
2. The sum variable is initialized to store the sum of factorials.
3. A copy of the number is stored in temp.
4. The while loop extracts each digit and calculates its factorial.
5. The sum of factorials is compared with the original number.
6. If they are equal, the number is a Strong Number, otherwise, it is not.

Alternative Approaches

Example 2: Using a For Loop

We can replace the while loop with a for loop for a cleaner approach.

# Python program to find Strong Number using for loop  
num = int(input("Enter the Number: "))  
sum = 0  
temp = num  
  
while temp > 0:  
    fact = 1  
    rem = temp % 10  
  
    for i in range(1, rem + 1):  
        fact *= i  
    
    print(f"Factorial of {rem} = {fact}")  
    sum += fact  
    temp //= 10  
  
print(f"\nSum of Factorials of {num} = {sum}")  
  
if sum == num:  
    print("The given number is a Strong Number")  
else:  
    print("The given number is not a Strong Number")  

Output:

Enter the Number: 145
Factorial of 5 = 120
Factorial of 4 = 24
Factorial of 1 = 1
Sum of Factorials of 145 = 145
The given number is a Strong Number

Example 3: Making Use of the Factorial Function in Python

To simplify the factorial calculation, we can use the math.factorial() function from Python’s math module.

import math  
num = int(input("Enter the Number: "))  
sum = 0  
temp = num  
  
while temp > 0:  
    rem = temp % 10  
    fact = math.factorial(rem)  # Using built-in factorial() function  
    print(f"Factorial of {rem} = {fact}")  
    sum += fact  
    temp //= 10  
  
print(f"\nSum of Factorials of {num} = {sum}")  
  
if sum == num:  
    print("The given number is a Strong Number")  
else:  
    print("The given number is not a Strong Number")  

Output:

Enter the Number: 145
Factorial of 5 = 120
Factorial of 4 = 24
Factorial of 1 = 1

Sum of Factorials of 145 = 145
The given number is a Strong Number.

Explanation

• The factorial was computed using the math.factorial() function.
• The loop keeps going until every digit has been handled.
• To ascertain whether the total is a strong number, it is compared to the original number.

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Conclusion

In this tutorial, we explored Strong Numbers and implemented different approaches using while loop, for loop, and math.factorial() function. The concept of Strong Numbers helps in understanding the use of loops, conditional statements, and factorial calculations in Python.

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