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  1214540585

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