# Check if a number is power of 8 or not

• Difficulty Level : Medium
• Last Updated : 21 Jun, 2022

Given a number check whether it is a power of 8 or not.

Examples :

```Input : n = 64
Output : Yes

Input : 75
Output : No```

First solution

We calculate log8(n) of the number if it is an integer, then n is in the power of 8. We use trunc(n) function that finds the closest integer for a double value.

## C++

 `// C++ program to check if a number is power of 8``#include ``#include ``using` `namespace` `std;` `/* function to check if power of 8 */``bool` `checkPowerof8(``int` `n)``{``    ``/* calculate log8(n) */``    ``double` `i = ``log``(n) / ``log``(8);` `    ``/* check if i is an integer or not */``    ``return` `(i - trunc(i) < 0.000001);``}` `/* driver function */``int` `main()``{``    ``int` `n = 65;``    ``checkPowerof8(n) ? cout << ``"Yes"` `: cout << ``"No"``;``    ``return` `0;``}`

## Java

 `// Java program to check if``// a number is power of 8` `class` `GFG {` `    ``// function to check``    ``// if power of 8``    ``static` `boolean` `checkPowerof8(``int` `n)``    ``{``        ``/* calculate log8(n) */``        ``double` `i = Math.log(n) / Math.log(``8``);` `        ``/* check if i is an integer or not */``        ``return` `(i - Math.floor(i) < ``0.000001``);``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `n = ``65``;``        ``if` `(checkPowerof8(n))``            ``System.out.println(``"Yes"``);``        ``else``            ``System.out.println(``"No"``);``    ``}``}` `// This code is contributed by Sam007`

## Python3

 `# Python3 program to check``# if a number is power of 8``from` `math ``import` `log,trunc` `# function to check if power of 8``def` `checkPowerof8(n):` `    ``# calculate log8(n)``    ``i ``=` `log(n, ``8``)` `    ``# check if i is an integer or not``    ``return` `(i ``-` `trunc(i) < ``0.000001``);` `# Driver Code``n ``=` `65``if` `checkPowerof8(n):``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)` `# This code is contributed by Mohit Kumar`

## C#

 `// C#  program to check if``// a number is power of 8``using` `System;` `class` `GFG {` `    ``// function to check``    ``// if power of 8``    ``static` `bool` `checkPowerof8(``int` `n)``    ``{` `        ``// calculate log8(n) */``        ``double` `i = Math.Log(n) / Math.Log(8);` `        ``// check if i is an integer or not */``        ``return` `(i - Math.Floor(i) < 0.000001);``    ``}` `    ``// Driver Code``    ``static` `public` `void` `Main()``    ``{``        ``int` `n = 65;` `        ``if` `(checkPowerof8(n))``            ``Console.WriteLine(``"Yes"``);``        ``else``            ``Console.WriteLine(``"No"``);``    ``}``}` `// This code is contributed by akt_mit`

## PHP

 ``

## Javascript

 ``

Output :

`No`

Time Complexity: O(1)

Auxiliary Space: O(1)

Second solution
A number is a power of 8 if the following conditions are satisfied.

1. The number is the power of two. A number is the power of two if it has only one set bit, i.e., bitwise and of n and n-1 is 0.
2. The number has its only set a bit at position 0 or 3 or 6 or …. 30 [For a 32-bit number]. To check the position of its set bit we can use a mask (0xB6DB6DB6)16 = (10110110110110110110110110110110)2.

Below is the implementation of the above idea.

## C++

 `// C++ program to check if a number is power of 8``// using bit mask.``#include ``using` `namespace` `std;` `/*function to check if power of 8*/``bool` `checkPowerof8(``int` `n)``{``    ``return` `(n && !(n & (n - 1)) && !(n & 0xB6DB6DB6));``}` `/*driver function*/``int` `main()``{``    ``int` `n = 65;``    ``checkPowerof8(n) ? cout << ``"Yes"` `: cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `// Java program to check if a``// number is power of 8 using``// bit mask.``import` `java.util.*;``class` `GFG{` `// function to check if``// power of 8``static` `boolean` `checkPowerof8(``int` `n)``{``  ``return` `(n > ``0` `&& (n & (n - ``1``)) > ``0` `&&``         ``(n & ``0xB6DB6DB6``) > ``0``);``}` `// Driver code``public` `static` `void` `main(String[] args)``{``  ``int` `n = ``65``;``  ``if` `(checkPowerof8(n) == ``true``)``    ``System.out.print(``"Yes"` `);``  ``else``    ``System.out.print(``"No"``);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to check if a number``# is power of 8` `# function to check if power of 8``def` `checkPowerof8(n):` `    ``return` `(n ``and` `not` `(n & (n ``-` `1``)) ``and``                  ``not` `(n & ``0xB6DB6DB6``))` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``n ``=` `65``    ` `if` `checkPowerof8(n):``    ``print` `(``"Yes"``) ``else``:``    ``print` `(``"No"``)` `# This code is contributed by ita_c`

## C#

 `// C# program to check if a``// number is power of 8 using``// bit mask.``using` `System;` `class` `GFG{``    ` `// Function to check if``// power of 8``static` `bool` `checkPowerof8(``int` `n)``{``    ``return` `(n > 0 && (n & (n - 1)) > 0 &&``           ``(n & 0xB6DB6DB6) > 0);``}` `// Driver code``static` `public` `void` `Main()``{``    ``int` `n = 65;``    ` `    ``if` `(checkPowerof8(n) == ``true``)``    ``{``        ``Console.WriteLine(``"Yes"``);``    ``}``    ``else``    ``{``        ``Console.WriteLine(``"No"``);``    ``}``}``}` `// This code is contributed by avanitrachhadiya2155`

## PHP

 ``

## Javascript

 ``

Output :

`No`

Time Complexity: O(1)

Auxiliary Space: O(1)

One simple observation that can be made here is that if a number is the power of 8 then it has only a one-bit set and that bit is at positions 1, 4, 7, 10, …
Thus, we can just check if the only bit set in the number is at one of these positions then it is a power of 8 otherwise not.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to check if n is power of 8``bool` `checkPowerof8(``int` `n)``{``    ``// Variable i will denote the bit``    ``// that we are currently at``    ``int` `i = 0;``    ``unsigned ``long` `long` `l = 1;``    ``while` `(i <= 63) {``        ``l <<= i;` `        ``// If only set bit in n``        ``// is at position i``        ``if` `(l == n)``            ``return` `true``;` `        ``// Get to next valid bit position``        ``i += 3;``        ``l = 1;``    ``}``    ``return` `false``;``}` `// Driver code``int` `main()``{``    ``int` `n = 65;``    ``if` `(checkPowerof8(n))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.io.*;` `class` `GFG``{``    ` `// Function to check if n is power of 8``static` `boolean` `checkPowerof8(``int` `n)``{``    ``// Variable i will denote the bit``    ``// that we are currently at``    ``int` `i = ``0``;``    ``long` `l = ``1``;``    ``while` `(i <= ``63``)``    ``{``        ``l <<= i;` `        ``// If only set bit in n``        ``// is at position i``        ``if` `(l == n)``            ``return` `true``;` `        ``// Get to next valid bit position``        ``i += ``3``;``        ``l = ``1``;``    ``}``    ``return` `false``;``}` `// Driver code``public` `static` `void` `main (String[] args)``{``    ` `    ``int` `n = ``65``;``    ``if` `(checkPowerof8(n))``        ``System.out.println (``"Yes"``);``    ``else``        ``System.out.println( ``"No"``);``}``}` `// This code is contributed by Tushil.`

## Python3

 `# Python3 implementation of the approach` `# Function to check if n is power of 8``def` `checkPowerof8(n):``    ` `    ``# Variable i will denote the bit``    ``# that we are currently at``    ``i ``=` `0``    ``l ``=` `1``    ` `    ``while` `(i <``=` `63``):``        ``l <<``=` `i` `        ``# If only set bit in n``        ``# is at position i``        ``if` `(l ``=``=` `n):``            ``return` `True` `        ``# Get to next valid bit position``        ``i ``+``=` `3``        ``l ``=` `1``  ` `    ``return` `False``  ` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``     ` `    ``n ``=` `65``    ``if` `(checkPowerof8(n)):``        ``print``(``"Yes"``)``    ``else``:``        ``print``(``"No"``)` `# This code is contributed by math_lover`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{``    ` `// Function to check if n is power of 8``static` `bool` `checkPowerof8(``int` `n)``{``    ``// Variable i will denote the bit``    ``// that we are currently at``    ``int` `i = 0;``    ``long` `l = 1;``    ``while` `(i <= 63)``    ``{``        ``l <<= i;` `        ``// If only set bit in n``        ``// is at position i``        ``if` `(l == n)``            ``return` `true``;` `        ``// Get to next valid bit position``        ``i += 3;``        ``l = 1;``    ``}``    ``return` `false``;``}` `// Driver code``static` `public` `void` `Main ()``{``    ``int` `n = 65;``    ``if` `(checkPowerof8(n))``        ``Console.WriteLine(``"Yes"``);``    ``else``        ``Console.WriteLine( ``"No"``);``}``}` `// This code is contributed by ajit.`

## Javascript

 ``

Output :

`No`

Time Complexity: O(1)

Auxiliary Space: O(1)

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