Giuga Number in Java

In this article, we will learn about Giuga Numbers and how to write a code to check if a number is a Giuga Number or not in Java. A Giuga number is a composite number N such that for each prime factor p of N, (N/p)-1 is divisible by p. The first Giuga numbers are 30, 858, 1722, 66198, 2214408306, 24423128562, and 432749205173838.

Example

Lets take N=30.
30 is a composite number, and its prime factors are 2, 3, and 5.
? For p=2:
(N/p)-1 to be divisible by p. N is 30, and p here is 2.
(30/2)-1=14, which is divisible by 2.
? For p=3:
(30/3) - 1 = 9, which is divisible by 3.
? For p=5:
(30/5)-1=5, which is divisible by 5.
Since the condition is true for all its prime factors, 30 is a Giuga number.

Algorithm

This step-by-step process helps check if a number is a Giuga number in a simple way.

1.Input a number N.

2.If N is prime, it is not a Giuga number, so return false. If N is composite, proceed with the next steps.

3.Find all the prime factors of N.

4.For every prime factor, do these two steps:

• Calculate (N/p) - 1
• Check the result is divisible by p.

5. If all prime factors pass these two steps, then N is a Giuga number, so return True.

Implementation code

The following Java program checks whether a given number is a Giuga number.

public class GiugaChecker {
   // Method to check if a number is prime
   public static boolean isPrimeNumber(int number) {
      if (number <= 1) return false; // Numbers <= 1 are not prime
      for (int i = 2; i * i <= number; i++) { 
         if (number % i == 0) return false; // If divisible, not prime
      }
      return true; // Otherwise, it's prime
   }
   // Method to check if a number is a Giuga number
   public static boolean isGiuga(int n) {
      if (isPrimeNumber(n)) return false; // Prime numbers can't be Giuga numbers
      // Check each prime factor of n
      for (int i = 2; i <= n / 2; i++) {
         if (isPrimeNumber(i) && n % i == 0) { // If i is a prime factor of n
            if ((n / i - 1) % i != 0) return false; // Condition fails, not Giuga
         }
      }
      return true; // Passes all checks, it's a Giuga number
   }
   // Main method to test the Giuga number checker
   public static void main(String[] args) {
      int number = 30; // Change this number to test different inputs

      // Check and display if the number is a Giuga number
      if (isGiuga(number)) {
         System.out.println(number + " is a Giuga number.");
      } else {
         System.out.println(number + " is not a Giuga number.");
      }
   }
}

Output

30 is a Giuga number.

Conclusion

In this article, we learned what Giuga numbers are and how to check if a number is a Giuga number or not with examples. We also learned about how to write Java code to implement the concept.