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Find the largest composite number that divides N but is strictly lesser than N

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  • Last Updated : 19 Oct, 2022
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Given a composite number N, the task is to find the largest composite number that divides N and is strictly lesser than N. If there is no such number exist print -1.
Examples: 

Input: N = 16 
Output:
Explanation: 
All numbers that divide 16 are { 1, 2, 4, 8, 16 } 
out of which 8 is largest composite number(lesser than 16) that divides 16.

Input: N = 100 
Output: -1

 

Approach: 
Since N is a composite number, therefore N can be the product of two numbers such that one is prime number and another is a composite number and if we can’t find such a pair for N then the largest composite number which is less than N that divides N doesn’t exist. 
To find the largest composite number find the smallest prime number(say a) that divides N. Then the largest composite number that divides N and less than N can be given by (N/a).

The following are the steps: 

  1. Find the smallest prime number of N (say a).
  2. Check if (N/a) is prime or not. If yes then we can’t find the largest composite number.
  3. Else (N/a) is the largest composite number that divides N and less than N.

Below is the implementation of the above approach: 

C++




// C++ program to find the largest
// composite number that divides
// N which is less than N
#include <bits/stdc++.h>
using namespace std;
 
// Function to check whether
// a number is prime or not
bool isPrime(int n)
{
    // Corner case
    if (n <= 1)
        return false;
 
    // Check from 2 to n-1
    for (int i = 2; i < n; i++)
        if (n % i == 0)
            return false;
 
    return true;
}
 
// Function that find the largest
// composite number which divides
// N and less than N
int getSmallestPrimefactor(int n)
{
    // Find the prime number
    for (int i = 2; i <= sqrt(n); i++) {
        if (n % i == 0)
            return i;
    }
}
 
// Driver's Code
int main()
{
    int N = 100;
    int a;
 
    // Get the smallest prime
    // factor
    a = getSmallestPrimefactor(N);
 
    // Check if (N/a) is prime
    // or not
    // If Yes print "-1"
    if (isPrime(N / a)) {
        cout << "-1";
    }
 
    // Else print largest composite
    // number (N/a)
    else {
        cout << N / a;
    }
    return 0;
}

Java




// Java program to find the largest
// composite number that divides
// N which is less than N
import java.util.*;
 
class GFG {
 
    // Function to check whether
    // a number is prime or not
    static boolean isPrime(int n)
    {
 
        // Corner case
        if (n <= 1)
            return false;
 
        // Check from 2 to n-1
        for (int i = 2; i < n; i++) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
 
    // Function that find the largest
    // composite number which divides
    // N and less than N
    static int getSmallestPrimefactor(int n)
    {
 
        // Find the prime number
        for (int i = 2; i <= Math.sqrt(n); i++) {
            if (n % i == 0)
                return i;
        }
        return -1;
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int N = 100;
        int a;
 
        // Get the smallest prime
        // factor
        a = getSmallestPrimefactor(N);
 
        // Check if (N/a) is prime or
        // not. If Yes print "-1"
        if (isPrime(N / a)) {
            System.out.print("-1");
        }
 
        // Else print largest composite
        // number (N/a)
        else {
            System.out.print(N / a);
        }
    }
}
 
// This code is contributed by amal kumar choubey

Python3




# Python3 program to find the largest
# composite number that divides
# N which is less than N
import math
 
# Function to check whether
# a number is prime or not
 
 
def isPrime(n):
 
    # Corner case
    if (n <= 1):
        return False
 
    # Check from 2 to n-1
    for i in range(2, n):
        if (n % i == 0):
            return False
 
    return True
 
# Function that find the largest
# composite number which divides
# N and less than N
 
 
def getSmallestPrimefactor(n):
 
    # Find the prime number
    for i in range(2, (int)(math.sqrt(n) + 1)):
        if (n % i == 0):
            return i
 
    return -1
 
 
# Driver Code
N = 100
 
# Get the smallest prime
# factor
a = getSmallestPrimefactor(N)
 
# Check if (N/a) is prime
# or not. If Yes print "-1"
if ((isPrime((int)(N / a)))):
    print(-1)
 
# Else print largest composite
# number (N/a)
else:
    print((int)(N / a))
 
# This code is contributed by grand_master

C#




// C# program to find the largest
// composite number that divides
// N which is less than N
using System;
class GFG {
 
    // Function to check whether
    // a number is prime or not
    static bool isPrime(int n)
    {
 
        // Corner case
        if (n <= 1)
            return false;
 
        // Check from 2 to n-1
        for (int i = 2; i < n; i++) {
            if (n % i == 0)
                return false;
        }
        return true;
    }
 
    // Function that find the largest
    // composite number which divides
    // N and less than N
    static int getSmallestPrimefactor(int n)
    {
 
        // Find the prime number
        for (int i = 2; i <= Math.Sqrt(n); i++) {
            if (n % i == 0)
                return i;
        }
        return -1;
    }
 
    // Driver Code
    public static void Main()
    {
        int N = 100;
        int a;
 
        // Get the smallest prime
        // factor
        a = getSmallestPrimefactor(N);
 
        // Check if (N/a) is prime or
        // not. If Yes print "-1"
        if (isPrime(N / a)) {
            Console.Write("-1");
        }
 
        // Else print largest composite
        // number (N/a)
        else {
            Console.Write(N / a);
        }
    }
}
 
// This code is contributed by Code_Mech

Javascript




<script>
 
// Javascript program to find the largest
// composite number that divides
// N which is less than N
 
// Function to check whether
// a number is prime or not
function isPrime(n)
{
    // Corner case
    if (n <= 1)
        return false;
     
    var i;
    // Check from 2 to n-1
    for (i = 2; i < n; i++)
        if (n % i == 0)
            return false;
 
    return true;
}
 
// Function that find the largest
// composite number which divides
// N and less than N
function getSmallestPrimefactor(n)
{
     var i;
    // Find the prime number
    for (i = 2; i <= Math.sqrt(n); i++) {
        if (n % i == 0)
            return i;
    }
}
 
// Driver's Code
 
    var N = 100;
    var a;
 
    // Get the smallest prime
    // factor
    a = getSmallestPrimefactor(N);
 
    // Check if (N/a) is prime
    // or not
    // If Yes print "-1"
    if (isPrime(N / a))
        document.write("-1");
 
    // Else print largest composite
    // number (N/a)
    else
        document.write(N/a);
 
</script>

Output: 

50

 

Time Complexity: O(sqrt(N))
Auxiliary space: O(1)


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