Giuga numbers in JavaA Giuga Number is a composite number N that has a unique property. The property states that for every prime factor, p of N, N divided by p minus 1 ((N/p)  1) should also be divisible by p. If a number N satisfies this condition for all its prime factors, it is considered a Giuga Number. To check if a given number N is a Giuga Number, you need to verify this property for all its prime factors. If it holds true for every prime factor, the number N is classified as a Giuga Number, and the output is "Yes". If the property does not hold for its prime factors, the number is not a Giuga Number, and the result is "No". Here are a few more examples to illustrate the concept of Giuga Numbers: Example 1: Input: N = 24 Output: No Explanation: 24 is a composite number with prime divisors {2, 3}. 2 does not divide 24 / 2  1 = 11, and 3 does not divide 24 / 3  1 = 7. Example 2: Input: N = 56 Output: No Explanation: 56 is a composite number with prime divisors {2, 7}. 2 does not divide 56 / 2  1 = 27 7 divides 56 / 7  1 = 7. Example 3: Input: N = 49 Output: No Explanation: 49 is a composite number with a prime divisor {7}. 7 does not divide 49 / 7  1 = 6 Example 4: Input: N = 30 Output: Yes Explanation: 30 is a composite number with prime divisors {2, 3, 5}. 2 divides 30 / 2  1 = 14, 3 divides 30 / 3  1 = 9, 5 divides 30 / 5  1 = 5. Approach: Brute Force ApproachIn this approach, the code iterates through all numbers from 2 to (N1) to check if each i satisfies the Giuga Number property. It checks whether i is prime, N is divisible by i, and (N/i  1) is divisible by i for each i. If all conditions hold true for at least one i, the number N is not considered a Giuga Number. If no such i is found, N is regarded as a Giuga Number. Algorithm:Step 1: Create a method called isPrime(number) that determines whether a given number is prime. Step 2: When the provided number gets less than or equal to 1, return false since numbers within this range are not considered prime. Step 3: Iterate from 2 to the square root of the given number:
Step 4: When no divisors have been identified during the loop, return true, indicating that the integer is a prime number. Step 5: Create a method isGiugaNumber(n) to check if a given number is a Giuga Number. Step 6: If the input number is prime, return false, as prime numbers cannot be Giuga Numbers. Step 7: Iterate through integers from 2 to the input number minus one:
Step 8: If no such i is found that breaks the Giuga Number property, return false to indicate that the number does not satisfy the Giuga Number property. Implementation:Filename: GiugaNumberChecker.java Output: 30 is a Giuga number. Time Complexity: O(n^{2}), where n is the input number. Space Complexity: O(1)
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