Special Number in Java

In this section, we will learn what is a special number and also create Java programs to check if the given number is a special number or not. The special number program frequently asked in Java coding tests and academics.

Special Number

If the sum of the factorial of digits of a number (N) is equal to the number itself, the number (N) is called a special number.

Let's understand it through an example.

Special Number Example

Consider a number 145 and check it is a special number or not.

The digits of the number are: 1, 4, 5

Factorial of digits:

!1 = 1

!4 = 4*3*2*1 = 24

!5 = 5*4*3*2*1 = 120

Sum of factorial of digits = 1 + 24 + 120 = 145

Compare the sum of the factorial of digits with the given number, i.e. 145 = 145. We observe that both are equal.

Hence, the given number 145 is a special number.

Let's check another number 1034.

The digits of the number are: 1, 0, 3, 4

Factorial of digits:

!1 = 1

!0 = 1

!3 = 3*2*1 = 6

!4 = 4*3*2*1 =24

Sum of factorial of digits = 1 + 1 + 6 + 24 = 32

Compare the sum of the factorial of digits with the given number, i.e. 32 ≠ 1034. We observe that the sum of factorial of digits is not equal to the given number.

Hence, the given number 1034 is not a special number.

Some other special numbers are 2, 40585, etc.

Steps to Find Special Number

Read or initialize a number (N).
Split the given number (N) into digits if the number has more than one digit.
Find the factorial of all digits.
Sum up the factorial and store it in a variable (s).
Compare the sum with the given number (N).
If the sum is equal to the number itself, the number (N) is a special number, else not.

Let's implement the above logic in a Java program.

Special Number Java Program

SpecialNumberExample1.java

import java.util.Scanner;
public class SpecialNumberExample1
{
public static void main(String args[])
{
int num, number, last_digit, sum_Of_Fact = 0;
Scanner sc = new Scanner(System.in);
System.out.print("Enter a number: ");
//reads an integer from the user
number = sc.nextInt();
num = number;
//executes until the condition becomes false
while (number > 0)
{
//finds the alst digit from the given number    
last_digit = number % 10;
//variable stores factorial 
int fact=1;
//factorial logic
for(int i=1; i<=last_digit; i++)
{
//calculates factorial     
fact=fact*i;
}
//calculates the sum of all factorials
sum_Of_Fact = sum_Of_Fact + fact;
//divides the number by 10 and removes the last digit from the number
number = number / 10;
}
//compares the sum with the given number
if(num==sum_Of_Fact)
{
System.out.println(num+ " is a special number.");
}
else
{
System.out.println(num+ " is not a special number.");
}
}
}

Output 1:

Enter a number: 40585
40585 is a special number.

Output 2:

Enter a number: 176
176 is not a special number.

Special Number Within a Range

SpecialNumberExample2.java

import java.util.Scanner;
public class SpecialNumberExample2
{
//Array with factorials of 0 to 9
static int factorial[] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880};
public static void main(String args[]) 
{
Scanner in = new Scanner(System.in);
boolean hasSpecial = false;
//Enter the range values
System.out.print("Enter the lower range: ");
//reads the lower range 
int lower_range = in.nextInt();
System.out.print("Enter the upper range: ");
//reads the upper range
int upper_range = in.nextInt();
//iterates over the given range
for(int i=lower_ranger; i<=upper_range; i++)
{
//use isSpecial() method to check if it is special
if(isSpecialNumber(i))
{
//prints the special number    
System.out.print(i+"\t");
hasSpecial = true;
}
}
//executes if the specified range does not have any special number
if(!hasSpecial)
System.out.println("No special numbers found.");
}
//function checks if the number is special or not, if special returns true
private static boolean isSpecialNumber(int n)
{
int digit, sum=0, temp=n;
//Extract digits and sum their factorial
while(temp != 0)
{
//find digits     
digit = temp%10;
//finds sum of factorials
sum = sum + factorial[digit];
//removes the last digit from the number
temp = temp/10;
}
//returns true if sum==n, else returns false
return sum == n;
}
}

Output:

Enter the lower range: 1
Enter the upper range: 100000
1	2	145	40585

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