In this tutorial, we will start by learning what is Sphenic Number and write a Java Program to check for the Sphenic Number.
Sphenic Number
A Sphenic Number is a positive integer n which is a product of exactly three distinct prime numbers. Or we can say that n is a sphenic integer if n = a * b * c (a, b, and c are three distinct prime numbers and their product is equal to n).
Example: 30, 42, 66, 70, 78, 102, 105, etc.
Explanation:
1 2 3 4 5 6 7 8 | Input : <strong>110</strong> Output : Yes <strong>Explanation </strong>: Factors of 110 are = 1, 2, 5, 10, 11, 22,55 and 110 Take the smallest three prime factors: <strong>2, 5, 11</strong> Product of these smallest prime factors: <strong>2*5*11</strong> = <strong>110</strong> = Input =<strong>110</strong> Hence the number is Sphenic Number. |
Java Program to Check if the Number is Sphenic Number or not
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 | import java.util.*; public class SphenicNumberExample1 { static boolean arr[] = new boolean[10000]; static void findPrime() { Arrays.fill(arr, true); for (int p = 2; p * p < 10000; p++) { //if p is not changed, then it is a prime if (arr[p]) { for (int i = p * 2; i < 10000; i = i + p) arr[i] = false; } } } //checks if the given number is sphenic or not static int isSphenic(int N) { int[] arr1 = new int[8]; int count = 0, j = 0; for (int i = 1; i <= N; i++) { if (N % i == 0 && count < 8) { //increments the count by 1 count++; arr1[j++] = i; } } if (count == 8 && (arr[arr1[1]] && arr[arr1[2]] && arr[arr1[3]])) return 1; return 0; } //main function public static void main(String args[]) { int n, result; findPrime(); Scanner sc = new Scanner(System.in); System.out.print("Enter a number: "); n = sc.nextInt(); result = isSphenic(n); if (result == 1) System.out.print(n + " is a sphenic Number."); else System.out.print(n + " is not a sphenic Number."); } } |
Output:
//First Execution
Enter a number: 30
30 is a sphenic Number.
//Second Execution
Enter a number: 165
165 is a sphenic Number.