Composite Number

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.
?>

Javascript

<script>

// A optimized school method based Javascript 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 (let 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

    isComposite(11)? document.write(" true" + "<br>"): document.write(" false" + "<br>");
    isComposite(15)? document.write(" true" + "<br>"): document.write(" false" + "<br>");


// This code is contributed by Mayank Tyagi

</script>

Output: 

false
true

Time Complexity:- O(sqrt(n))

Space Complexity:-O(1)

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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