# Program to find whether a no is power of two

Given a positive integer, write a function to find if it is a power of two or not.
Examples :

```Input : n = 4
Output : Yes
22 = 4

Input : n = 7
Output : No

Input : n = 32
Output : Yes
25 = 32
```

1. A simple method for this is to simply take the log of the number on base 2 and if you get an integer then the number is the power of

## C++

 `// C++ Program to find whether a` `// no is power of two` `#include` `using` `namespace` `std;`   `// Function to check if x is power of 2` `bool` `isPowerOfTwo(``int` `n)` `{` `   ``if``(n==0)` `   ``return` `false``;`   `   ``return` `(``ceil``(log2(n)) == ``floor``(log2(n)));` `}`   `// Driver program` `int` `main()` `{` `    ``isPowerOfTwo(31)? cout<<``"Yes"``<

## C

 `// C Program to find whether a` `// no is power of two` `#include` `#include` `#include`   `/* Function to check if x is power of 2*/` `bool` `isPowerOfTwo(``int` `n)` `{` `   ``if``(n==0)` `   ``return` `false``;`   `   ``return` `(``ceil``(log2(n)) == ``floor``(log2(n)));` `}`   `// Driver program` `int` `main()` `{` `    ``isPowerOfTwo(31)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);` `    ``isPowerOfTwo(64)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);` `    ``return` `0;` `}`   `// This code is contributed by bibhudhendra`

## Java

 `// Java Program to find whether a` `// no is power of two` `class` `GFG` `{` `/* Function to check if x is power of 2*/` `static` `boolean` `isPowerOfTwo(``int` `n)` `{` `    ``if``(n==``0``)` `    ``return` `false``;`   `return` `(``int``)(Math.ceil((Math.log(n) / Math.log(``2``)))) == ` `       ``(``int``)(Math.floor(((Math.log(n) / Math.log(``2``)))));` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``if``(isPowerOfTwo(``31``))` `    ``System.out.println(``"Yes"``);` `    ``else` `    ``System.out.println(``"No"``);` `    `  `    ``if``(isPowerOfTwo(``64``))` `    ``System.out.println(``"Yes"``);` `    ``else` `    ``System.out.println(``"No"``);` `}` `}`   `// This code is contributed by mits`

## Python3

 `# Python3 Program to find ` `# whether a no is ` `# power of two` `import` `math`   `# Function to check` `# Log base 2` `def` `Log2(x):` `    ``if` `x ``=``=` `0``:` `        ``return` `false;`   `    ``return` `(math.log10(x) ``/` `            ``math.log10(``2``));`   `# Function to check` `# if x is power of 2` `def` `isPowerOfTwo(n):` `    ``return` `(math.ceil(Log2(n)) ``=``=` `            ``math.floor(Log2(n)));`   `# Driver Code` `if``(isPowerOfTwo(``31``)):` `    ``print``(``"Yes"``);` `else``:` `    ``print``(``"No"``);`   `if``(isPowerOfTwo(``64``)):` `    ``print``(``"Yes"``);` `else``:` `    ``print``(``"No"``);` `    `  `# This code is contributed ` `# by mits`

## C#

 `// C# Program to find whether ` `// a no is power of two` `using` `System;`   `class` `GFG` `{` `    `  `/* Function to check if ` `   ``x is power of 2*/` `static` `bool` `isPowerOfTwo(``int` `n)` `{`   `    ``if``(n==0)` `     ``return` `false``;`   `    ``return` `(``int``)(Math.Ceiling((Math.Log(n) / ` `                               ``Math.Log(2)))) ==` `           ``(``int``)(Math.Floor(((Math.Log(n) / ` `                              ``Math.Log(2)))));` `}`   `// Driver Code` `public` `static` `void` `Main()` `{` `    ``if``(isPowerOfTwo(31))` `        ``Console.WriteLine(``"Yes"``);` `    ``else` `        ``Console.WriteLine(``"No"``);` `    `  `    ``if``(isPowerOfTwo(64))` `        ``Console.WriteLine(``"Yes"``);` `    ``else` `        ``Console.WriteLine(``"No"``);` `}` `}`   `// This code is contributed ` `// by Akanksha Rai(Abby_akku)`

## PHP

 ``

Output:

```No
Yes
```

2. Another solution is to keep dividing the number by two, i.e, do n = n/2 iteratively. In any iteration, if n%2 becomes non-zero and n is not 1 then n is not a power of 2. If n becomes 1 then it is a power of 2.

## C++

 `#include ` `using` `namespace` `std;`   `/* Function to check if x is power of 2*/` `bool` `isPowerOfTwo(``int` `n) ` `{ ` `    ``if` `(n == 0) ` `        ``return` `0; ` `    ``while` `(n != 1) ` `    ``{ ` `        ``if` `(n%2 != 0) ` `            ``return` `0; ` `        ``n = n/2; ` `    ``} ` `    ``return` `1; ` `} `   `/*Driver code*/` `int` `main() ` `{ ` `    ``isPowerOfTwo(31)? cout<<``"Yes\n"``: cout<<``"No\n"``; ` `    ``isPowerOfTwo(64)? cout<<``"Yes\n"``: cout<<``"No\n"``; ` `    ``return` `0; ` `} `   `// This code is contributed by rathbhupendra`

## C

 `#include` `#include`   `/* Function to check if x is power of 2*/` `bool` `isPowerOfTwo(``int` `n)` `{` `  ``if` `(n == 0)` `    ``return` `0;` `  ``while` `(n != 1)` `  ``{` `      ``if` `(n%2 != 0)` `         ``return` `0;` `      ``n = n/2;` `  ``}` `  ``return` `1;` `}`   `/*Driver program to test above function*/` `int` `main()` `{` `  ``isPowerOfTwo(31)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);` `  ``isPowerOfTwo(64)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);` `  ``return` `0;` `}`

## Java

 `// Java program to find whether` `// a no is power of two` `import` `java.io.*;`   `class` `GFG {`   `    ``// Function to check if ` `    ``// x is power of 2` `    ``static` `boolean` `isPowerOfTwo(``int` `n)` `    ``{` `        ``if` `(n == ``0``)` `            ``return` `false``;` `        `  `        ``while` `(n != ``1``)` `        ``{` `            ``if` `(n % ``2` `!= ``0``)` `                ``return` `false``;` `            ``n = n / ``2``;` `        ``}` `        ``return` `true``;` `    ``}`   `    ``// Driver program ` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``if` `(isPowerOfTwo(``31``))` `            ``System.out.println(``"Yes"``);` `        ``else` `            ``System.out.println(``"No"``);`   `        ``if` `(isPowerOfTwo(``64``))` `            ``System.out.println(``"Yes"``);` `        ``else` `            ``System.out.println(``"No"``);` `    ``}` `}`   `// This code is contributed by Nikita tiwari.`

## Python3

 `# Python program to check if given` `# number is power of 2 or not `   `# Function to check if x is power of 2` `def` `isPowerOfTwo(n):` `    ``if` `(n ``=``=` `0``):` `        ``return` `False` `    ``while` `(n !``=` `1``):` `            ``if` `(n ``%` `2` `!``=` `0``):` `                ``return` `False` `            ``n ``=` `n ``/``/` `2` `            `  `    ``return` `True`   `# Driver code` `if``(isPowerOfTwo(``31``)):` `    ``print``(``'Yes'``)` `else``:` `    ``print``(``'No'``)` `if``(isPowerOfTwo(``64``)):` `    ``print``(``'Yes'``)` `else``:` `    ``print``(``'No'``)`   `# This code is contributed by Danish Raza`

## C#

 `// C# program to find whether` `// a no is power of two` `using` `System;`   `class` `GFG` `{` `    `  `    ``// Function to check if ` `    ``// x is power of 2` `    ``static` `bool` `isPowerOfTwo(``int` `n)` `    ``{` `        ``if` `(n == 0)` `            ``return` `false``;` `        `  `        ``while` `(n != 1) {` `            ``if` `(n % 2 != 0)` `                ``return` `false``;` `                `  `            ``n = n / 2;` `        ``}` `        ``return` `true``;` `    ``}`   `    ``// Driver program ` `    ``public` `static` `void` `Main()` `    ``{` `        ``Console.WriteLine(isPowerOfTwo(31) ? ``"Yes"` `: ``"No"``);` `        ``Console.WriteLine(isPowerOfTwo(64) ? ``"Yes"` `: ``"No"``);`   `    ``}` `}`   `// This code is contributed by Sam007`

## PHP

 ``

Output :

```No
Yes

```

3. Another way is to use this simple recursive solution. It uses the same logic as the above iterative solution but uses recursion instead of iteration.

## C++

 `// C++ program for above approach` `#include ` `using` `namespace` `std;`   `// Function which checks whether a ` `// number is a power of 2` `bool` `powerOf2(``int` `n)` `{` `    ``// base cases` `    ``// '1' is the only odd number ` `    ``// which is a power of 2(2^0) ` `    ``if` `(n == 1) ` `      ``return` `true``; ` `    `  `    ``// all other odd numbers are not powers of 2` `    ``else` `if` `(n % 2 != 0 || n ==0) ` `      ``return` `false``; ` `    `  `    ``// recursive function call` `    ``return` `powerOf2(n / 2); ` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `n = 64;``//True` `    ``int` `m = 12;``//False`   `    ``if` `(powerOf2(n) == 1) ` `      ``cout << ``"True"` `<< endl;`   `    ``else` `cout << ``"False"` `<< endl;`   `    ``if` `(powerOf2(m) == 1) ` `      ``cout << ``"True"` `<< endl;`   `    ``else` `      ``cout << ``"False"` `<< endl;` `}`   `//code contributed by Moukthik a.k.a rowdyninja`

## Java

 `// Java program for ` `// the above approach` `import` `java.util.*;` `class` `GFG{`   `// Function which checks ` `// whether a number is a ` `// power of 2` `static` `boolean` `powerOf2(``int` `n)` `{` `  ``// base cases` `  ``// '1' is the only odd number ` `  ``// which is a power of 2(2^0) ` `  ``if` `(n == ``1``) ` `    ``return` `true``; `   `  ``// all other odd numbers are` `  ``// not powers of 2` `  ``else` `if` `(n % ``2` `!= ``0` `|| ` `           ``n ==``0``) ` `    ``return` `false``; `   `  ``// recursive function call` `  ``return` `powerOf2(n / ``2``); ` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `  ``//True` `  ``int` `n = ``64``;` `  `  `  ``//False` `  ``int` `m = ``12``;`   `  ``if` `(powerOf2(n) == ``true``) ` `    ``System.out.print(``"True"` `+ ``"\n"``);` `  ``else` `System.out.print(``"False"` `+ ``"\n"``);`   `  ``if` `(powerOf2(m) == ``true``) ` `    ``System.out.print(``"True"` `+ ``"\n"``);` `  ``else` `    ``System.out.print(``"False"` `+ ``"\n"``);` `}` `}`   `// This code is contributed by Princi Singh`

## Python3

 `# Python program for above approach`   `# function which checks whether a ` `# number is a power of 2 ` `def` `powerof2(n):` `  `  `    ``# base cases` `    ``# '1' is the only odd number ` `    ``# which is a power of 2(2^0)` `    ``if` `n ``=``=` `1``: ` `        ``return` `True` `    `  `    ``# all other odd numbers are not powers of 2` `    ``elif` `n``%``2` `!``=` `0` `or` `n ``=``=` `0``: ` `        ``return` `False` `    `  `    ``#recursive function call` `    ``return` `powerof2(n``/``2``) ` `  `  `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:` `  `  `  ``print``(powerof2(``64``)) ``#True` `  ``print``(powerof2(``12``)) ``#False` `  `  `#code contributed by Moukthik a.k.a rowdyninja`

## C#

 `// C# program for above approach` `using` `System;`   `class` `GFG{` `    `  `// Function which checks whether a ` `// number is a power of 2` `static` `bool` `powerOf2(``int` `n)` `{` `    `  `    ``// Base cases` `    ``// '1' is the only odd number ` `    ``// which is a power of 2(2^0) ` `    ``if` `(n == 1) ` `      ``return` `true``; ` `     `  `    ``// All other odd numbers ` `    ``// are not powers of 2` `    ``else` `if` `(n % 2 != 0 || n == 0) ` `      ``return` `false``; ` `     `  `    ``// Recursive function call` `    ``return` `powerOf2(n / 2); ` `}`   `// Driver code ` `static` `void` `Main() ` `{` `  `  `    ``int` `n = 64;``//True` `    ``int` `m = 12;``//False` `    `  `    ``if` `(powerOf2(n)) ` `    ``{` `        ``Console.Write(``"True"` `+ ``"\n"``);` `    ``}` `    ``else` `    ``{` `        ``Console.Write(``"False"` `+ ``"\n"``);` `    ``}` `    `  `    ``if` `(powerOf2(m)) ` `    ``{` `        ``Console.Write(``"True"``);` `    ``}` `    ``else` `    ``{` `        ``Console.Write(``"False"``);` `    ``}` `}` `}`   `// This code is contributed by rutvik_56`

Output

```True
False

```

4. All power of two numbers has only a one-bit set. So count the no. of set bits and if you get 1 then the number is a power of 2. Please see Count set bits in an integer for counting set bits.

5. If we subtract a power of 2 numbers by 1 then all unset bits after the only set bit become set; and the set bit becomes unset.
For example for 4 ( 100) and 16(10000), we get the following after subtracting 1
3 –> 011
15 –> 01111

So, if a number n is a power of 2 then bitwise & of n and n-1 will be zero. We can say n is a power of 2 or not based on the value of n&(n-1). The expression n&(n-1) will not work when n is 0. To handle this case also, our expression will become n& (!n&(n-1)) (thanks to https://www.geeksforgeeks.org/program-to-find-whether-a-no-is-power-of-two/Mohammad for adding this case).

Below is the implementation of this method.

## C++

 `#include ` `using` `namespace` `std;` `#define bool int `   `/* Function to check if x is power of 2*/` `bool` `isPowerOfTwo (``int` `x) ` `{ ` `    ``/* First x in the below expression is for the case when x is 0 */` `    ``return` `x && (!(x&(x-1))); ` `} `   `/*Driver code*/` `int` `main() ` `{ ` `    ``isPowerOfTwo(31)? cout<<``"Yes\n"``: cout<<``"No\n"``; ` `    ``isPowerOfTwo(64)? cout<<``"Yes\n"``: cout<<``"No\n"``; ` `    ``return` `0; ` `} `   `// This code is contributed by rathbhupendra`

## C

 `#include` `#define bool int`   `/* Function to check if x is power of 2*/` `bool` `isPowerOfTwo (``int` `x)` `{` `  ``/* First x in the below expression is for the case when x is 0 */` `  ``return` `x && (!(x&(x-1)));` `}`   `/*Driver program to test above function*/` `int` `main()` `{` `  ``isPowerOfTwo(31)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);` `  ``isPowerOfTwo(64)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);` `  ``return` `0;` `}`

## Java

 `// Java program to efficiently ` `// check for power for 2`   `class` `Test` `{` `    ``/* Method to check if x is power of 2*/` `    ``static` `boolean` `isPowerOfTwo (``int` `x)` `    ``{` `      ``/* First x in the below expression is ` `        ``for the case when x is 0 */` `        ``return` `x!=``0` `&& ((x&(x-``1``)) == ``0``);` `        `  `    ``}` `    `  `    ``// Driver method` `    ``public` `static` `void` `main(String[] args) ` `    ``{` `         ``System.out.println(isPowerOfTwo(``31``) ? ``"Yes"` `: ``"No"``);` `         ``System.out.println(isPowerOfTwo(``64``) ? ``"Yes"` `: ``"No"``);` `        `  `    ``}` `}` `// This program is contributed by Gaurav Miglani    `

## Python

 `# Python program to check if given` `# number is power of 2 or not `   `# Function to check if x is power of 2` `def` `isPowerOfTwo (x):`   `    ``# First x in the below expression ` `    ``# is for the case when x is 0 ` `    ``return` `(x ``and` `(``not``(x & (x ``-` `1``))) )`   `# Driver code` `if``(isPowerOfTwo(``31``)):` `    ``print``(``'Yes'``)` `else``:` `    ``print``(``'No'``)` `    `  `if``(isPowerOfTwo(``64``)):` `    ``print``(``'Yes'``)` `else``:` `    ``print``(``'No'``)` `    `  `# This code is contributed by Danish Raza    `

## C#

 `// C# program to efficiently ` `// check for power for 2` `using` `System;`   `class` `GFG` `{` `    ``// Method to check if x is power of 2` `    ``static` `bool` `isPowerOfTwo (``int` `x)` `    ``{` `        ``// First x in the below expression  ` `        ``// is for the case when x is 0 ` `        ``return` `x != 0 && ((x & (x - 1)) == 0);` `        `  `    ``}` `    `  `    ``// Driver method` `    ``public` `static` `void` `Main() ` `    ``{` `        ``Console.WriteLine(isPowerOfTwo(31) ? ``"Yes"` `: ``"No"``);` `        ``Console.WriteLine(isPowerOfTwo(64) ? ``"Yes"` `: ``"No"``);` `        `  `    ``}` `}`   `// This code is contributed by Sam007`

## PHP

 ``

Output :

```No
Yes

```