A composite number is a positive integer that is not prime. In other words, it has a positive divisor other than one or itself. First few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ………
- Every integer greater than one is either a prime number or a composite number.
- The number one is a unit – it is neither prime nor composite.
How to check if a given number is a composite number or not?
Examples:
Input : n = 21 Output: Yes The number is a composite number! Input : n = 11 Output : No
The idea is simple, we can use any of the below methods used for prime checking. We just need to change return statements. Return true is changed to return false and vice versa.
- Primality Test | Set 1 (Introduction and School Method)
- Primality Test | Set 2 (Fermat Method)
- Primality Test | Set 3 (Miller–Rabin)
In below code optimized school method is discussed.
C++
// A optimized school method based C++ program to check // if a number is composite. #include <bits/stdc++.h> using namespace std; bool isComposite(int n) { // Corner cases if (n <= 1) return false; if (n <= 3) return false; // This is checked so that we can skip // middle five numbers in below loop if (n%2 == 0 || n%3 == 0) return true; for (int i=5; i*i<=n; i=i+6) if (n%i == 0 || n%(i+2) == 0) return true; return false; } // Driver Program to test above function int main() { isComposite(11)? cout << " true\n": cout << " false\n"; isComposite(15)? cout << " true\n": cout << " false\n"; return 0; } |
Java
/// An optimized method based Java // program to check if a number // is Composite or not. import java.io.*; class Composite { static boolean isComposite(int n) { // Corner cases if (n <= 1) System.out.println("False"); if (n <= 3) System.out.println("False"); // This is checked so that we can skip // middle five numbers in below loop if (n % 2 == 0 || n % 3 == 0) return true; for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return true; return false; } // Driver Program to test above function public static void main(String args[]) { System.out.println(isComposite(11) ? "true" : "false"); System.out.println(isComposite(15) ? "true" : "false"); } } // This code is contributed by Anshika Goyal |
Python 3
# A optimized school method based Python program to check # if a number is composite. def isComposite(n): # Corner cases if (n <= 1): return False if (n <= 3): return False # This is checked so that we can skip # middle five numbers in below loop if (n % 2 == 0 or n % 3 == 0): return True i = 5 while(i * i <= n): if (n % i == 0 or n % (i + 2) == 0): return True i = i + 6 return False # Driver Program to test above function print("true") if(isComposite(11)) else print("false") print("true") if(isComposite(15)) else print("false") # This code is contributed by Anant Agarwal. |
C#
// A optimized school method based C# program // to check if a number is composite. using System; namespace Composite { public class GFG { public static bool isComposite(int n) { // Corner cases if (n <= 1) return false; if (n <= 3) return false; // This is checked so that we can skip // middle five numbers in below loop if (n % 2 == 0 || n % 3 == 0) return true; for (int i = 5; i * i <= n; i = i + 6) if (n % i == 0 || n % (i + 2) == 0) return true; return false; } // Driver Code public static void Main() { if(isComposite(11)) Console.WriteLine("true"); else Console.WriteLine("false"); if(isComposite(15)) Console.WriteLine("true"); else Console.WriteLine("false"); } } } // This code is contributed by Sam007 |
PHP
<?php // A optimized school // method based PHP // program to check // if a number is composite. function isComposite($n) { // Corner cases if ($n <= 1) return false; if ($n <= 3) return false; // This is checked so // that we can skip // middle five numbers // in below loop if ($n%2 == 0 || $n % 3 == 0) return true; for ($i = 5; $i * $i <= $n; $i = $i + 6) if ($n % $i == 0 || $n % ($i + 2) == 0) return true; return false; } // Driver Code if(isComposite(11)) echo "true"; else echo "false"; echo"\n"; if(isComposite(15)) echo "true"; else echo "false"; echo"\n"; // This code is contributed by Ajit. ?> |
Output:
false true
Program on Composite Numbers
- Find a range of composite numbers of given length
- Generate a list of n consecutive composite numbers (An interesting method)
- Sum and product of k smallest and k largest composite numbers in the array
- Product of all the Composite Numbers in an array
- Count and Sum of composite elements in an array
- Split n into maximum composite numbers
Reference :
https://en.wikipedia.org/wiki/Composite_number
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