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: 8
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:
- Find the smallest prime number of N (say a).
- Check if (N/a) is prime or not. If yes then we can’t find the largest composite number.
- Else (N/a) is the largest composite number that divides N and less than N.
Below is the implementation of the above approach:
// 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 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 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# 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 |
<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> |
50
Time Complexity: O(sqrt(N))
Auxiliary space: O(1)