Number with maximum number of prime factors

Given an integer N. The task is to find a number that is smaller than or equal to N and has maximum prime factors. In case there are two or more numbers with same maximum number of prime factors, find the smallest of all.

Examples:

Input : N = 10
Output : 6
Number of prime factor of:
1 : 0
2 : 1
3 : 1
4 : 1
5 : 1
6 : 2
7 : 1
8 : 1
9 : 1
10 : 2
6 and 10 have maximum (2) prime factor
but 6 is smaller.

Input : N = 40
Output : 30

Method 1 (brute force):
For each integer from 1 to N, find the number of prime factor of each integer and find the smallest number having maximum number of prime factors.

Method 2 (Better Approach):
Use sieve method to count number of prime factor of each number less than N. And find the minimum number having maximum count.

Below is the implementation of this approach:

C++

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// C++ program to find integer having maximum number
// of prime factor in first N natural numbers.
#include<bits/stdc++.h>
  
using namespace std;
  
// Return smallest number having maximum
// prime factors.
int maxPrimefactorNum(int N)
{
    int arr[N + 5];
    memset(arr, 0, sizeof(arr));
  
    // Sieve of eratosthenes method to count
    // number of prime factors.
    for (int i = 2; i*i <= N; i++)
    {
        if (!arr[i])
            for (int j = 2*i; j <= N; j+=i)
                arr[j]++;
  
        arr[i] = 1;
    }
  
    int maxval = 0, maxint = 1;
  
    // Finding number having maximum number
    // of prime factor.
    for (int i = 1; i <= N; i++)
    {
        if (arr[i] > maxval)
        {
            maxval = arr[i];
            maxint = i;
        }
    }
  
    return maxint;
}
  
// Driven Program
int main()
{
    int N = 40;
    cout << maxPrimefactorNum(N) << endl;
    return 0;
}

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Java

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// Java program to find integer having maximum number 
// of prime factor in first N natural numbers. 
import java.util.Arrays;
public class GFG {
  
// Return smallest number having maximum 
// prime factors. 
    static int maxPrimefactorNum(int N) {
        int arr[] = new int[N + 5];
        Arrays.fill(arr, 0);
          
        // Sieve of eratosthenes method to count 
        // number of prime factors. 
        for (int i = 2; i * i <= N; i++) {
            if (arr[i] == 0) {
                for (int j = 2 * i; j <= N; j += i) {
                    arr[j]++;
                }
            }
  
            arr[i] = 1;
        }
  
        int maxval = 0, maxint = 1;
  
        // Finding number having maximum number 
        // of prime factor. 
        for (int i = 1; i <= N; i++) {
            if (arr[i] > maxval) {
                maxval = arr[i];
                maxint = i;
            }
        }
  
        return maxint;
    }
// Driver program 
  
    public static void main(String[] args) {
        int N = 40;
        System.out.println(maxPrimefactorNum(N));
    }
}

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Python3

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# Python 3 program to find integer having 
# maximum number of prime factor in first 
# N natural numbers.
from math import sqrt
  
# Return smallest number having maximum
# prime factors.
def maxPrimefactorNum(N):
    arr = [0 for i in range(N + 5)]
  
    # Sieve of eratosthenes method to
    # count number of prime factors.
    for i in range(2, int(sqrt(N)) + 1, 1):
        if (arr[i] == 0):
            for j in range(2 * i, N + 1, i):
                arr[j] += 1
  
        arr[i] = 1
  
    maxval = 0
    maxint = 1
  
    # Finding number having maximum 
    # number of prime factor.
    for i in range(1, N + 1, 1):
        if (arr[i] > maxval):
            maxval = arr[i]
            maxint = i
      
    return maxint
  
# Driver Code
if __name__ == '__main__':
    N = 40
    print(maxPrimefactorNum(N))
  
# This code is contributed by
# Sahil_Shelangia

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C#

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// C# program to find integer having 
// maximum number of prime factor in
// first N natural numbers.
using System;
  
class GFG 
  
// Return smallest number having 
// prime factors. 
static int maxPrimefactorNum(int N)
    int []arr = new int[N + 5]; 
      
    // Sieve of eratosthenes method to 
    // count number of prime factors. 
    for (int i = 2; i * i <= N; i++)
    
        if (arr[i] == 0) 
        
            for (int j = 2 * i; j <= N; j += i)
            
                arr[j]++; 
            
        
  
        arr[i] = 1; 
    
  
    int maxval = 0, maxint = 1; 
  
    // Finding number having maximum 
    // number of prime factor. 
    for (int i = 1; i <= N; i++) 
    
        if (arr[i] > maxval) 
        
            maxval = arr[i]; 
            maxint = i; 
        
    
  
    return maxint; 
  
// Driver Code 
public static void Main()
    int N = 40; 
    Console.WriteLine(maxPrimefactorNum(N)); 
  
// This code is contributed 
// by 29AjayKumar

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PHP

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<?php
// PHP program to find integer having 
// maximum number of prime factor in
// first N natural numbers. 
  
// Return smallest number having
// maximum prime factors. 
function maxPrimefactorNum($N
    $arr[$N + 5] = array(); 
    $arr = array_fill(0, $N + 1, NULL);
      
    // Sieve of eratosthenes method to count 
    // number of prime factors. 
    for ($i = 2; ($i * $i) <= $N; $i++) 
    
        if (!$arr[$i]) 
            for ($j = 2 * $i; $j <= $N; $j += $i
                $arr[$j]++; 
  
        $arr[$i] = 1; 
    
  
    $maxval = 0;
    $maxint = 1; 
  
    // Finding number having maximum
    // number of prime factor. 
    for ($i = 1; $i <= $N; $i++) 
    
        if ($arr[$i] > $maxval
        
            $maxval = $arr[$i]; 
            $maxint = $i
        
    
  
    return $maxint
  
// Driver Code
$N = 40; 
echo maxPrimefactorNum($N), "\n";
  
// This code is contributed by ajit
?>

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Output:

30

Method 3 (efficient approach):
Generate all prime number before N using Sieve. Now, multiply consecutive prime numbers (starting from first prime number) one after another until the product is less than N.

Below is the implementation of this approach:

C++

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// C++ program to find integer having maximum number
// of prime factor in first N natural numbers
#include<bits/stdc++.h>
  
using namespace std;
  
// Return smallest number having maximum prime factors.
int maxPrimefactorNum(int N)
{
    bool arr[N + 5];
    memset(arr, true, sizeof(arr));
  
    // Sieve of eratosthenes
    for (int i = 3; i*i <= N; i += 2)
    {
        if (arr[i])
            for (int j = i*i; j <= N; j+=i)
                arr[j] = false;
    }
  
    // Storing prime numbers.
    vector<int> prime;
    prime.push_back(2);
  
    for(int i = 3; i <= N; i += 2)
        if(arr[i])
            prime.push_back(i);
  
    // Generating number having maximum prime factors.
    int i = 0, ans = 1;
    while (ans*prime[i] <= N && i < prime.size())
    {
        ans *= prime[i];
        i++;
    }
  
    return ans;
}
  
// Driven Program
int main()
{
    int N = 40;
    cout << maxPrimefactorNum(N) << endl;
    return 0;
}

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Java

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// Java program to find integer having maximum number 
// of prime factor in first N natural numbers 
import java.util.Vector;
  
public class GFG {
  
// Return smallest number having maximum prime factors.
    static int maxPrimefactorNum(int N) {
        //default value of boolean is false
        boolean arr[] = new boolean[N + 5];
  
        // Sieve of eratosthenes 
        for (int i = 3; i * i <= N; i += 2) {
            if (!arr[i]) {
                for (int j = i * i; j <= N; j += i) {
                    arr[j] = true;
                }
            }
        }
  
        // Storing prime numbers. 
        Vector<Integer> prime = new Vector<>(); 
        prime.add(prime.size(), 2);
        for (int i = 3; i <= N; i += 2) {
            if (!arr[i]) {
                prime.add(prime.size(), i);
            }
        }
  
        // Generating number having maximum prime factors. 
        int i = 0, ans = 1;
        while (ans * prime.get(i) <= N && i < prime.size()) {
            ans *= prime.get(i);
            i++;
        }
  
        return ans;
    }
// Driver program 
  
    public static void main(String[] args) {
        int N = 40;
        System.out.println(maxPrimefactorNum(N));
    }
}

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Python3

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# Python3 program to find integer having 
# maximum number of prime factor in first
# N natural numbers
  
# Return smallest number having 
# maximum prime factors.
def maxPrimefactorNum(N):
  
    arr = [True] * (N + 5);
  
    # Sieve of eratosthenes
    i = 3;
    while (i * i <= N):
        if (arr[i]):
            for j in range(i * i, N + 1, i):
                arr[j] = False;
        i += 2;
  
    # Storing prime numbers.
    prime = [];
    prime.append(2);
  
    for i in range(3, N + 1, 2):
        if(arr[i]):
            prime.append(i);
  
    # Generating number having maximum 
    # prime factors.
    i = 0;
    ans = 1;
    while (ans * prime[i] <= N and 
                    i < len(prime)):
        ans *= prime[i];
        i += 1;
  
    return ans;
  
# Driver Code
N = 40;
print(maxPrimefactorNum(N));
  
# This code is contributed by mits

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C#

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// C# program to find integer having maximum number 
// of prime factor in first N natural numbers 
using System;
using System.Collections;
  
class GFG { 
  
    // Return smallest number having maximum prime factors. 
    static int maxPrimefactorNum(int N)
    
        //default value of boolean is false 
        bool []arr = new bool[N + 5]; 
        int i ;
          
        // Sieve of eratosthenes 
        for (i = 3; i * i <= N; i += 2) 
        
            if (!arr[i]) 
            
                for (int j = i * i; j <= N; j += i)
                
                    arr[j] = true
                
            
        
  
        // Storing prime numbers. 
        ArrayList prime = new ArrayList(); 
        prime.Add(2); 
        for (i = 3; i <= N; i += 2) 
        
            if (!arr[i])
            
                prime.Add(i); 
            
        
  
        // Generating number having 
        // maximum prime factors. 
        int ans = 1; 
        i = 0;
        while (ans * (int)prime[i] <= N && i < prime.Count)
        
            ans *= (int)prime[i]; 
            i++; 
        
  
        return ans; 
    
  
    // Driver code
    public static void Main() 
    
        int N = 40; 
        Console.Write(maxPrimefactorNum(N)); 
    
  
// This code is contributed by Rajput-Ji 

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PHP

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<?php
// PHP program to find integer having maximum number
// of prime factor in first N natural numbers
  
// Return smallest number having 
// maximum prime factors.
function maxPrimefactorNum($N)
{
    $arr = array_fill(0, $N + 5, true);
  
    // Sieve of eratosthenes
    for ($i = 3; $i * $i <= $N; $i += 2)
    {
        if ($arr[$i])
            for ($j = $i * $i; $j <= $N; $j += $i)
                $arr[$j] = false;
    }
  
    // Storing prime numbers.
    $prime = array();
    array_push($prime, 2);
  
    for($i = 3; $i <= $N; $i += 2)
        if($arr[$i])
            array_push($prime, $i);
  
    // Generating number having maximum 
    // prime factors.
    $i = 0;
    $ans = 1;
    while ($ans * $prime[$i] <= $N && 
                  $i < count($prime))
    {
        $ans *= $prime[$i];
        $i++;
    }
  
    return $ans;
}
  
// Driver Code
$N = 40;
print(maxPrimefactorNum($N));
  
// This code is contributed by mits
?>

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Output:

30

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