Strong Number in Python

In this tutorial, we will learn a Python program to find a given number is a Strong number or not.

What is a strong number?

A Strong number is a special number whose sum of the all digit factorial should be equal to the number itself.

To find a whether given number is strong or not. We pick each digit from the given number and find its factorial, and we will do this every digit of the number.

Once we get the factorial of all digit, then we do the sum of factorials. If the sum is equal to the given number then the given number is strong otherwise not.

For example - The given number is 145, we have to pick each digit and find the factorial 1! = 1, 4! = 24, and 5! = 120.

Now, we will do the sum of the factorials, we get 1+24+120 = 145, which is exactly the same as the given number. So we can say that 145 is a strong number.

We got the logic of the strong number. Now implements it using the Python Program.

Problem Approach

Ask the user to enter an integer number.
Find the factorial of each digit in the number using the two while loop.
Now, sum up all the factorial number.
Check if it is equal to the given number.
Print the Output.
Exit

Sample Input: num = 132

Sample Output: Given number is not a strong number

Explanation: 1! + 3! + 2! = 9 which is not equal to the 132

Sample Input: num = 145

Sample Output: Given number is a strong number.

Python Program to Find Strong Number

Below is the code of the Python program to print the given number is a strong or not.

Example -

# Variable to store sum of the numbers
sum=0
# Ask user to enter the number
num=int(input("Enter a number:"))
# temporary variable  store copy of the original number
temp=num
# Using while loop
while(num):
    # intialize with 1
    i=1
    # fact variable with 1
    fact=1
    rem=num%10
    while(i<=rem):
        fact=fact*i   # Find factorial of each number
        i=i+1
    sum=sum+fact
    num=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:

In the above code

We declared a variable integer value num for enter a number.
Defined the sum variable with zero.
A copy of the num value to the temp variable.
In the first while loop, ensure that the given number is greater than 0.
Inside the while loop, split the number and assigns the variable to find the factorial of each number.
In the second while loop (nested while loop), finds the factorial of the each number.

Suppose user enter the value = 145 and sum = 0

Assigning initial values

i = 0
fact = 0
temp = num
temp = 145

Now understand the loop iteration. First Iteration

rem = temp % 10
rem = 145 % 10 = 5

Now, we entered in the nested while loop. It calculates the factorial of 5 is 120.

sum = sum + 120> 0+120
sum = 120
temp = temp//10 = 14
temp = 14

Second Iteration

temp = 14,
sum = 120
rem = 14 % 10 = 4

Now, it enters into nested While loop. Here, it calculates the factorial of 4 = 24.

sum = 120 + 24
sum = 144

temp = 14//10   
temp = 1

Third Iteration

temp = 1 
sum = 144
rem = 1 % 10 = 0

The factorial of 1 is 1

sum = 144 + 1
sum = 145
temp = 1 / 10
temp = 0

Here, the temp = 0 so, the while loop condition fails.

If (num == sum) Now, we check the condition whether the user enter number is exactly equal to sum or not. If this condition returns True, then it is strong Number, else it is not Strong Number.

We have complete the program using the while loop. We can also use for loop to find whether a given number is strong or not.

Strong Number Using the for loop

We can also find the strong number using for loop. The logic is the same as above program, the while loop is replaced by for loop.

Example -

# Python Program to find Strong Number
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 = fact * i

    print("Factorial of %d = %d" %(rem, fact))
    sum = sum + fact
    temp = temp // 10

print("\n Sum of Factorials of a Given Number %d = %d" %(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 a Given Number 145 = 145
The given number is a Strong Number

Python Program to find strong number using factorial function

Python math module provides the built-in math module. By using this method, we can omit the use of the nested while loop.

Example -

# Python Program to find Strong Number

import math
num = int(input(" Enter the Number:"))
sum = 0
temp = num

while(temp > 0):
    rem = temp % 10
    fact = math.factorial(rem)  # Using the buitlt-in factorial() function

    print("Factorial of %d = %d" %(rem, fact))
    sum = sum + fact
    temp = temp // 10

print("\n Sum of Factorials of a Given Number %d = %d" %(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 a Given Number 145 = 145
 The given number is a Strong Number

Explanation -

In the above code,

We used the factorial() function and passed a reminder as an argument.
In the first iteration of while loop, it returned the reminder 5 and passed to the factorial of 5.
It will go on until the temp value is greater than zero. We don't need to use another while loop.

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