Greatest odd factor of an even number

Given an even number N, the task is to find the greatest possible odd factor of N.

Examples: 

Input: N = 8642 
Output: 4321 
Explanation:
Here, factors of 8642 are {1, 8642, 2, 4321, 29, 298, 58, 149} in which odd factors are {1, 4321, 29, 149} and the greatest odd factor among all odd factors is 4321.

Input: N = 100 
Output: 25 
Explanation:
Here, factors of 100 are {1, 100, 2, 50, 4, 25, 5, 20, 10} in which odd factors are {1, 25, 5} and the greatest odd factor among all odd factors is 25. 

Naive Approach: The naive approach is to find all the factors of N and then select the greatest odd factor from it. 
Time Complexity: O(sqrt(N))

Efficient Approach: The efficient approach for this problem is to observe that every even number N can be represented as:  

N = 2i*odd_number

Therefore to get the largest odd number we need to divide the given number N by 2 until N becomes an odd number.

Below is the implementation of the above approach:  

C++

// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;

// Function to print greatest odd factor
int greatestOddFactor(int n)
{
    int pow_2 = (int)(log(n));

    // Initialize i with 1
    int i = 1;

    // Iterate till i <= pow_2
    while (i <= pow_2)
    {

        // Find the pow(2, i)
        int fac_2 = (2 * i);
        if (n % fac_2 == 0)
        {
            // If factor is odd, then
            // print the number and break
            if ((n / fac_2) % 2 == 1)
            {
                return (n / fac_2);
            }
        }

        i += 1;
    }
}

// Driver Code
int main()
{

    // Given Number
    int N = 8642;

    // Function Call
    cout << greatestOddFactor(N);
    return 0;
}

// This code is contributed by Amit Katiyar

Java

// Java program for the above approach
class GFG{

// Function to print greatest odd factor
public static int greatestOddFactor(int n)
{
    int pow_2 = (int)(Math.log(n));

    // Initialize i with 1
    int i = 1;

    // Iterate till i <= pow_2
    while (i <= pow_2)
    {

        // Find the pow(2, i)
        int fac_2 = (2 * i);
        if (n % fac_2 == 0)
        {

            // If factor is odd, then
            // print the number and break
            if ((n / fac_2) % 2 == 1)
            {
                return (n / fac_2);
            }
        }
        i += 1;
    }
    return 0;
}

// Driver code
public static void main(String[] args)
{

    // Given Number
    int N = 8642;

    // Function Call
    System.out.println(greatestOddFactor(N));
}
}

// This code is contributed by divyeshrabadiya07

Python3

# Python3 program for the above approach

# importing Maths library
import math

# Function to print greatest odd factor
def greatestOddFactor(n):

  pow_2 = int(math.log(n, 2))

# Initialize i with 1
  i = 1

# Iterate till i <= pow_2
  while i <= pow_2:

# find the pow(2, i)
    fac_2 = (2**i)

    if (n % fac_2 == 0) :

      # If factor is odd, then print the
      # number and break
      if ( (n // fac_2) % 2 == 1):
        print(n // fac_2)
        break

    i += 1

# Driver Code

# Given Number
N = 8642

# Function Call
greatestOddFactor(N)

C#

// C# program for the above approach
using System;

class GFG{

// Function to print greatest odd factor
public static int greatestOddFactor(int n)
{
    int pow_2 = (int)(Math.Log(n));

    // Initialize i with 1
    int i = 1;

    // Iterate till i <= pow_2
    while (i <= pow_2)
    {

        // Find the pow(2, i)
        int fac_2 = (2 * i);
        if (n % fac_2 == 0)
        {

            // If factor is odd, then
            // print the number and break
            if ((n / fac_2) % 2 == 1)
            {
                return (n / fac_2);
            }
        }
        i += 1;
    }
    return 0;
}

// Driver code
public static void Main(String[] args)
{

    // Given number
    int N = 8642;

    // Function call
    Console.WriteLine(greatestOddFactor(N));
}
}

// This code is contributed by gauravrajput1

Javascript

<script>

// JavaScript program for the above approach

// Function to print greatest odd factor
function greatestOddFactor(n)
{
    let pow_2 = (Math.log(n));

    // Initialize i with 1
    let i = 1;

    // Iterate till i <= pow_2
    while (i <= pow_2)
    {

        // Find the pow(2, i)
        let fac_2 = (2 * i);
        if (n % fac_2 == 0)
        {

            // If factor is odd, then
            // print the number and break
            if ((n / fac_2) % 2 == 1)
            {
                return (n / fac_2);
            }
        }
        i += 1;
    }
    return 0;
}


// Driver Code

    // Given Number
    let N = 8642;

    // Function Call
    document.write(greatestOddFactor(N)); ;

</script>

Output:

4321

Time Complexity: O(log2(N))
Auxiliary Space: O(1)