# 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 untill N becomes an odd number.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach  ` `#include  ` `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 `

Output:

```4321
```

Time Complexity: O(log2(N))

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