Strong Number in Python

What is a Strong Number?

If the sum of the factorial of all the digits of a number is equal to the number itself, that number is called a Strong Number.

Confused? Okay, I'll find a better way to explain this.

Take any number, for instance, let us take $145$. This number contains the digits $1$, $4$, and $5$, their factorials will be $1$, $24$, and $120$ respectively, and the total sum of the factorials would be $1+24+120=145$. The sum of the factorial of all the digits is equal to the number itself. Therefore, the number $145$ is a strong number.

Now, let us look at another example for clarity.

This time, we will take the number $154$. This number contains the digits $1$, $5$, and $4$, their factorials will be $1$, $120$, and $24$ respectively, and the total sum of the factorials would be $1+120+24=145$. The sum of the factorial of all the digits is not equal to the number itself. Therefore, the number $154$ is not a strong number :disappointed:.

Programs to Check if the Given Number is a Strong number in Python

In Python, there are various methods to check if a number is a strong number or not. Let us look at each of them:

Python Program to Check for Strong Number Using a While Loop

In this program, we will check for strong numbers using a while loop nested inside another while loop. The parent while loop is used to check for the strong number, and the nested while loop is used to calculate the factorial of a digit.

Steps of the Algorithm

1. Initialize $sum$ variable to be $0$.
2. Initialize $temp$ variable to be $n$.
3. Run a while loop till $temp$ is not $0$.
4. Inside the while loop, assign $rem$ to be $temp\%10$, initialize variables $x$ and $facto$ to be $1$.
5. Run a nested while loop while $x$ is less than or equal to $rem$ inside the main while loop.
6. Inside the nested while loop, multiply $facto$ by $x$ and increment $x$ by $1$ in each iteration.
7. After the end of the nested while loop, add $facto$ to $sum$ and divide $temp$ by $10$.
8. End the main while loop.
9. Check if $sum$ is equal to $n$, if yes, return True.
10. Return false.

Implementation

Output 1

Output 2

Explanation

In output 1, the inputted number is $145$. This number contains the digits $1$, $4$, and $5$, their factorials will be $1$, $24$, and $120$ respectively, and the total sum of the factorials would be $1+24+120=145$. The sum of the factorial of all the digits is equal to the number itself. Therefore, the number $145$ is a strong number, as can be seen in the output.

In output 2, the inputted number is $154$. This number contains the digits $1$, $5$, and $4$, their factorials will be $1$, $120$, and $24$ respectively, and the total sum of the factorials would be $1+120+24=145$. The sum of the factorial of all the digits is equal to the number itself. Therefore, the number $154$ is not a strong number, as can be seen in the output.

Python Program to Check for Strong Number Using a For Loop and a Dictionary (Pre-Determined Factorials)

In this program, we will check for strong numbers using a for loop and a dictionary.
The for loop will be used for checking strong numbers and the dictionary will be used to store the factorial of digits from $0$ to $9$.

Steps of the Algorithm

At first, create a dictionary $facto$ to store the factorial of digits from $0$ to $9$, where the key will be the digit and the value will be its factorial.

The isStrong() function

1. Initialize $sum$ variable to be $0$.
2. Iterate over the number (by typecasting it into a string) using a for loop, add facto[int(x)] to sum in each iteration.
3. Check if $sum$ is equal to $n$, if yes, return True.
4. Return false.

Implementation

Output 1

Output 2

Explanation

In output 1, the inputted number is $2$. This number contains a single digit $2$, its factorial will be $2$, and the total sum of the factorials would be $2$. The sum of the factorial of all the digits is equal to the number itself. Therefore, the number $2$ is a strong number, as can be seen in the output.

In output 2, the inputted number is $30$. This number contains the digits $3$, and $0$, their factorials will be $6$ and $0$ respectively, and the total sum of the factorials would be $6+0=6$. The sum of the factorial of all the digits is not equal to the number itself. Therefore, the number $30$ is not a strong number, as can be seen in the output.

Python Program to Check for Strong Number Using Recursion

In this program, we will check for a strong number using recursion. There will be two recursive functions in this program, isStrong() for checking strong numbers and factorial() for calculating the factorial of a number.

Steps of the Algorithm

The $factorial()$ function It returns the factorial of the number $n$ passed to it.

1. Check if $n$ is less than or equal to $1$, if yes, return $1$.
2. If no, return $n * factorial(n - 1)$.

Initialize a global variable $sum$ to be $0$.

The $isStrong()$ function
It returns $True$ or $False$ for a given number $n$ is a strong number or not.

1. Check if $n$ is not equal to $0$, if true, assign $rem$ to be $n \% 10$, $facto$ to be $factorial(rem)$, add $facto$ to $sum$, and lastly, call the $isStrong()$ function by passing $n//10$ to it.
2. Check if $sum$ is equal to $n$, if yes, return True.
3. Return false.

Implementation

Output 1

Output 2

Explanation

In output 1, the inputted number is $40585$. This number contains the digits $4$, $0$, $5$, $8$, and $5$, their factorials will be $24$, $0$, $120$, $40320$, and $120$ respectively, and the total sum of the factorials would be $24 + 0 + 120 + 40320 + 120 = 40585$. The sum of the factorial of all the digits is equal to the number itself. Therefore, the number $40585$ is a strong number, as can be seen in the output.

In output 2, the inputted number is $40844$. This number contains the digits $4$, $0$, $8$, $4$, and $4$, their factorials will be $24$, $0$, $40320$, $24$, and $24$ respectively, and the total sum of the factorials would be $24 + 0 + 40320 + 24 + 24 = 40392$. The sum of the factorial of all the digits is not equal to the number itself. Therefore, the number $40844$ is not a strong number, as can be seen in the output.

Python Program to Check for Strong Number Using the Math factorial() Function

In this program, we will check for the strong numbers using a while loop, inside which we will use the math factorial() function to calculate the factorial of a digit.

Steps of the Algorithm

Import math module.

The $isStrong()$ function

1. Initialize $sum$ variable to be $0$.
2. Initialize $temp$ variable to be $n$.
3. Run a while loop till $temp$ is not $0$.
4. Inside the while loop, assign $rem$ to be $temp\%10$.
5. Assign $facto$ to be $math.factorial(rem)$.
6. Add $facto$ to $sum$ and divide $temp$ by $10$.
7. End the while loop.
8. Check if $sum$ is equal to $n$, if yes, return True.
9. Return False.

Implementation

Output 1

Output 2

Explanation

In output 1, the inputted number is $1$. This number contains a single digit $1$, its factorial will be $1$, and the total sum of the factorials would be $1$. The sum of the factorial of all the digits is equal to the number itself. Therefore, the number $1$ is a strong number, as can be seen in the output.

In output 2, the inputted number is $91$. This number contains the digits $9$ and $1$, their factorials will be $362880$ and $1$ respectively, and the total sum of the factorials would be $362880 + 1 = 362881$. The sum of the factorial of all the digits is not equal to the number itself. Therefore, the number $91$ is not a strong number, as can be seen in the output.

Check out this article to learn about Math Module in Python.

Read More:

• Sum() in Python.