Find whether a given number is a power of 4 or not

Given an integer n, find whether it is a power of 4 or not.

Example :

Input : 16
Output : 16 is a power of 4

Input : 20
Output : 20 is not a power of 4

We strongly recommend that you click here and practice it, before moving on to the solution.

Method 1: Using the in-built log method: Take log of given number to the base 4, and then raise 4 to this result. If the output is equal to n, then given number is a power of 4, else not.

C++

// C++ program to find whether a given
// number is a power of 4 or not
#include<bits/stdc++.h>

using namespace std;

class GFG
{

/* Function to check if x is power of 4*/
public : bool isPowerOfFour(int n)
{
    if(n == pow(4, (int)(log(n)/log(4))) && n != 0)
        return true;
    return false;
}
};

/*Driver code*/
int main()
{
    GFG g;
    int test_no = 64;
    if(g.isPowerOfFour(test_no))
        cout << test_no << " is a power of 4";
    else
        cout << test_no << " is not a power of 4";
}

// This code is contributed by devendra123world

Java

// Java program to find whether a given number is a power of
// 4 or not

import java.io.*;

class GFG {

    // Function to check if x is a power of 4
    public boolean isPowerOfFour(int n)
    {
        if (n != 0 && n == (int)Math.pow(4, (Math.log(n) / Math.log(4)))) {
            return true;
        }
        return false;
    }

    public static void main(String[] args)
    {
        GFG g = new GFG();
        int test_no = 64;
        if (g.isPowerOfFour(test_no)) {
            System.out.print(test_no + " is a power of 4 ");
        }
        else {
            System.out.print(test_no
                             + " is not a power of 4");
        }
    }
}

// This code is contributed by lokesh (lokeshmvs21).

C#

// C# program to find whether a given number is a power of 4
// or not.

using System;

public class GFG {

    // Function to check if x is power of 4
    public bool isPowerOfFour(int n)
    {
        if (n != 0 && n == Math.Pow(4, (Math.Log(n) / Math.Log(4)))) {
            return true;
        }
        return false;
    }

    static public void Main()
    {

        // Code
        GFG g = new GFG();
        int test_no = 64;
        if (g.isPowerOfFour(test_no)) {
            Console.Write(test_no + " is a power of 4");
        }
        else {
            Console.Write(test_no + " is not a power of 4");
        }
    }
}

// This code is contributed by lokesh (lokeshmvs21)

Python3

# Python program to find whether a given number is a power of 4 or not.

import math


# Function to check if x is power of 4
def isPowerOfFour(n):
    if (n != 0 and n == pow(4, (math.log(n)/math.log(4)))):
        return True
    return False


test_no = 64
if(isPowerOfFour(test_no)):
    print(test_no, ' is a power of 4')
else:
    print(test_no, ' is not a power of 4')


# This code is contributed by lokesh (lokeshmvs21).

Javascript

<script>
// Function to check if x is power of 4
public bool isPowerOfFour(int n)
{
    if (n != 0 && n == Math.Pow(4, (Math.Log(n) / Math.Log(4)))) {
        return true;
    }
    return false;
}

static public void Main()
{

    // Code
    GFG g = new GFG();
    int test_no = 64;
    if (g.isPowerOfFour(test_no)) {
        document.write(test_no + " is a power of 4");
    }
    else {
        document.write(test_no + " is not a power of 4");
    }

    // This code is contributed by ksrikanth0498.
    </script>

Output

64 is a power of 4

Time Complexity: O(log(log₂(n))*log₂(n))
Auxiliary Space: O(1)

Method 2: Another solution is to keep dividing the number by 4, i.e, do n = n/4 iteratively. In any iteration, if n%4 becomes non-zero and n is not 1 then n is not a power of 4, otherwise, n is a power of 4. 

C++

// C++ program to find whether a given
// number is a power of 4 or not
#include<iostream>

using namespace std;
#define bool int

class GFG
{

/* Function to check if x is power of 4*/
public : bool isPowerOfFour(int n)
{
    if(n == 0)
        return 0;
    while(n != 1)
    {
        if(n % 4 != 0)
            return 0;
        n = n / 4;
    }
    return 1;
}
};

/*Driver code*/
int main()
{
    GFG g;
    int test_no = 64;
    if(g.isPowerOfFour(test_no))
        cout << test_no << " is a power of 4";
    else
        cout << test_no << "is not a power of 4";
    getchar();
}

// This code is contributed by SoM15242

C

#include<stdio.h>
#define bool int

/* Function to check if x is power of 4*/
bool isPowerOfFour(int n)
{
  if(n == 0)
    return 0;
  while(n != 1)
  {
   if(n % 4 != 0)
      return 0;
    n = n / 4;
  }
  return 1;
}

/*Driver program to test above function*/
int main()
{
  int test_no = 64;
  if(isPowerOfFour(test_no))
    printf("%d is a power of 4", test_no);
  else
    printf("%d is not a power of 4", test_no);
  getchar();
}

Java

// Java code to check if given
// number is power of 4 or not

class GFG {

    // Function to check if
    // x is power of 4
    static int isPowerOfFour(int n)
    {
        if(n == 0)
        return 0;
        while(n != 1)
        {
            if(n % 4 != 0)
            return 0;
            n = n / 4;
        }
        return 1;
    }

    // Driver program
    public static void main(String[] args)
    {
        int test_no = 64;
        if(isPowerOfFour(test_no) == 1)
         System.out.println(test_no +
                           " is a power of 4");
        else
         System.out.println(test_no +
                           "is not a power of 4");
    }
}

// This code is contributed
// by  prerna saini

Python3

# Python3 program to check if given
# number is power of 4 or not

# Function to check if x is power of 4
def isPowerOfFour(n):
    if (n == 0):
        return False
    while (n != 1):
            if (n % 4 != 0):
                return False
            n = n // 4

    return True

# Driver code
test_no = 64
if(isPowerOfFour(64)):
    print(test_no, 'is a power of 4')
else:
    print(test_no, 'is not a power of 4')

# This code is contributed by Danish Raza

C#

// C# code to check if given
// number is power of 4 or not
using System;

class GFG {

    // Function to check if
    // x is power of 4
    static int isPowerOfFour(int n)
    {
        if (n == 0)
            return 0;
        while (n != 1) {
            if (n % 4 != 0)
                return 0;
            n = n / 4;
        }
        return 1;
    }

    // Driver code
    public static void Main()
    {
        int test_no = 64;
        if (isPowerOfFour(test_no) == 1)
            Console.Write(test_no +
                    " is a power of 4");
        else
            Console.Write(test_no +
                " is not a power of 4");
    }
}

// This code is contributed by Sam007

PHP

<?php
// PHP code to check if given
// number is power of 4 or not

// Function to check if
// x is power of 4
function isPowerOfFour($n)
{

    if($n == 0)
        return 0;
    while($n != 1)
    {
        if($n % 4 != 0)
            return 0;
            $n = $n / 4;
    }
    return 1;
}

// Driver Code
$test_no = 64;

if(isPowerOfFour($test_no))
    echo $test_no," is a power of 4";
else
    echo $test_no," is not a power of 4";

// This code is contributed by Rajesh
?>

Javascript

<script>

/* Function to check if x is power of 4*/
function isPowerOfFour( n)
{
  if(n == 0)
    return false;
  while(n != 1)
  {
   if(n % 4 != 0)
      return false;
    n = n / 4;
  }
  return true;
}

/*Driver program to test above function*/
let test_no = 64;
  if(isPowerOfFour(test_no))
    document.write(test_no+" is a power of 4");
  else
    document.write(test_no+" is not a power of 4");

// This code is contributed by gauravrajput1

</script>

Output

64 is a power of 4

Time Complexity: O(log₄n)
Auxiliary Space: O(1)

Method 3: A number n is a power of 4 if the following conditions are met. 
a) There is only one bit set in the binary representation of n (or n is a power of 2) 
b) The count of zero bits before the (only) set bit is even.
For example 16 (10000) is the power of 4 because there is only one bit set and count of 0s before the set bit is 4 which is even.
Thanks to Geek4u for suggesting the approach and providing the code. 

C++

// C++ program to check
// if given number is
// power of 4 or not
#include<bits/stdc++.h>

using namespace std;

bool isPowerOfFour(unsigned int n)
{
    int count = 0;

    /*Check if there is only one bit set in n*/
    if ( n && !(n&(n-1)) )
    {
        /* count 0 bits before set bit */
        while(n > 1)
        {
            n >>= 1;
            count += 1;
        }

        /*If count is even then
        return true else false*/
        return (count%2 == 0)? 1 :0;
    }

    /* If there are more than 1 bit set
    then n is not a power of 4*/
    return 0;
}

/*Driver code*/
int main()
{
    int test_no = 64;
    if(isPowerOfFour(test_no))
        cout << test_no << " is a power of 4" ;
    else
        cout << test_no << " is not a power of 4";
}

// This code is contributed by Shivi_Aggarwal

C

#include<stdio.h>
#define bool int

bool isPowerOfFour(unsigned int n)
{
  int count = 0;

  /*Check if there is only one bit set in n*/
  if ( n && !(n&(n-1)) )
  {
     /* count 0 bits before set bit */
     while(n > 1)
     {
       n  >>= 1;
       count += 1;
     }

    /*If count is even then return true else false*/
    return (count%2 == 0)? 1 :0;
  }

  /* If there are more than 1 bit set
    then n is not a power of 4*/
  return 0;
}

/*Driver program to test above function*/
int main()
{
   int test_no = 64;
   if(isPowerOfFour(test_no))
     printf("%d is a power of 4", test_no);
   else
     printf("%d is not a power of 4", test_no);
   getchar();
}

Java

// Java program to check
// if given number is
// power of 4 or not
import java.io.*;
class GFG
{
    static int isPowerOfFour(int n)
    {
        int count = 0;

        /*Check if there is
        only one bit set in n*/
        int x = n & (n - 1);

        if ( n > 0 && x == 0)
        {
            /* count 0 bits
            before set bit */
            while(n > 1)
            {
                n >>= 1;
                count += 1;
            }

            /*If count is even
            then return true
            else false*/
            return (count % 2 == 0) ? 1 : 0;
        }

            /* If there are more than
            1 bit set then n is not a
            power of 4*/
        return 0;
    }

    // Driver Code
    public static void main(String[] args)
    {
        int test_no = 64;

        if(isPowerOfFour(test_no)>0)
            System.out.println(test_no +
                               " is a power of 4");
        else
            System.out.println(test_no +
                               " is not a power of 4");
    }
}

// This code is contributed by mits

Python3

# Python3 program to check if given
# number is power of 4 or not

# Function to check if x is power of 4
def isPowerOfFour(n):

    count = 0

    # Check if there is only one
    # bit set in n
    if (n and (not(n & (n - 1)))):

        # count 0 bits before set bit
        while(n > 1):
            n >>= 1
            count += 1

        # If count is even then return
        # true else false
        if(count % 2 == 0):
            return True
        else:
            return False

# Driver code
test_no = 64
if(isPowerOfFour(64)):
    print(test_no, 'is a power of 4')
else:
    print(test_no, 'is not a power of 4')

# This code is contributed by Danish Raza

C#

// C# program to check if given
// number is power of 4 or not
using System;

class GFG {

    static int isPowerOfFour(int n)
    {
        int count = 0;

        /*Check if there is only one bit
        set in n*/
        int x = n & (n-1);

        if ( n > 0 && x == 0)
        {
            /* count 0 bits before set bit */
            while(n > 1)
            {
                n >>= 1;
                count += 1;
            }

            /*If count is even then return
            true else false*/
            return (count % 2 == 0) ? 1 : 0;
        }

            /* If there are more than 1 bit set
            then n is not a power of 4*/
        return 0;
    }

    /*Driver program to test above function*/
    static void Main()
    {
        int test_no = 64;

        if(isPowerOfFour(test_no)>0)
            Console.WriteLine("{0} is a power of 4",
                                          test_no);
        else
            Console.WriteLine("{0} is not a power of 4",
                                             test_no);
    }
}

// This Code is Contributed by mits

PHP

<?php

function isPowerOfFour($n)
{
    $count = 0;

/*Check if there is only one bit set in n*/
if ( $n && !($n&($n-1)) )
{
    /* count 0 bits before set bit */
    while($n > 1)
    {
    $n >>= 1;
    $count += 1;
    }

    /*If count is even then return true else false*/
    return ($count%2 == 0)? 1 :0;
}

/* If there are more than 1 bit set
    then n is not a power of 4*/
return 0;
}

/*Driver program to test above function*/

    $test_no = 64;

if(isPowerOfFour($test_no))

    echo $test_no, " is a power of 4";

else

    echo $test_no, " not is a power of 4";


#This Code is Contributed by Ajit
?>

Javascript

<script>

// javascript program to check
// if given number is
// power of 4 or not

function isPowerOfFour( n)
{
    let count = 0;

    /*Check if there is only one bit set in n*/
    if ( n && !(n&(n-1)) )
    {
        /* count 0 bits before set bit */
        while(n > 1)
        {
            n >>= 1;
            count += 1;
        }

        /*If count is even then
        return true else false*/
        return (count%2 == 0)? 1 :0;
    }

    /* If there are more than 1 bit set
    then n is not a power of 4*/
    return 0;
}

/*Driver code*/
    let test_no = 64;
    if(isPowerOfFour(test_no))
       document.write( test_no +" is a power of 4" );
    else
        document.write(test_no + " is not a power of 4");


// This code contributed by aashish1995

</script>

Output

64 is a power of 4

Time Complexity: O(log₄n)
Auxiliary Space: O(1)

Method 4: A number n is a power of 4 if the following conditions are met. 
a) There is only one bit set in the binary representation of n (or n is a power of 2) 
b) The bits don’t AND(&) any part of the pattern 0xAAAAAAAA
For example: 16 (10000) is power of 4 because there is only one bit set and 0x10 & 0xAAAAAAAA is zero.
Thanks to Sarthak Sahu for suggesting the approach. 

C++

// C++ program to check
// if given number is
// power of 4 or not
#include<bits/stdc++.h>

using namespace std;

bool isPowerOfFour(unsigned int n)
{
    return n !=0 && ((n&(n-1)) == 0) && !(n & 0xAAAAAAAA);
}

/*Driver code*/
int main()
{
    int test_no = 64;
    if(isPowerOfFour(test_no))
        cout << test_no << " is a power of 4" ;
    else
        cout << test_no << " is not a power of 4";
}

C

// C program to check
// if given number is
// power of 4 or not
#include<stdio.h>
#define bool int

bool isPowerOfFour(unsigned int n)
{
  return n != 0 && ((n&(n-1)) == 0) && !(n & 0xAAAAAAAA);
}

/*Driver program to test above function*/
int main() {
   int test_no = 64;
   if(isPowerOfFour(test_no))
     printf("%d is a power of 4", test_no);
   else
     printf("%d is not a power of 4", test_no);
   getchar();
}

Java

// Java program to check
// if given number is
// power of 4 or not
import java.io.*;
class GFG {
    static boolean isPowerOfFour(int n) {
        return n != 0 && ((n&(n-1)) == 0) && (n & 0xAAAAAAAA) == 0;
    }

    // Driver Code
    public static void main(String[] args) {
        int test_no = 64;

        if(isPowerOfFour(test_no))
            System.out.println(test_no +
                               " is a power of 4");
        else
            System.out.println(test_no +
                               " is not a power of 4");
    }
}

Python3

# Python3 program to check
# if given number is
# power of 4 or not
def isPowerOfFour(n):
    return (n != 0 and
          ((n & (n - 1)) == 0) and
            not(n & 0xAAAAAAAA));

# Driver code
test_no = 64;
if(isPowerOfFour(test_no)):
    print(test_no ,"is a power of 4");
else:
    print(test_no , "is not a power of 4");

# This code contributed by Rajput-Ji

C#

// C# program to check
// if given number is
// power of 4 or not
using System;

class GFG
{
    static bool isPowerOfFour(int n)
    {
        return n != 0 && ((n&(n-1)) == 0) &&
                        (n & 0xAAAAAAAA) == 0;
    }

    // Driver Code
    static void Main()
    {
        int test_no = 64;

        if(isPowerOfFour(test_no))
            Console.WriteLine("{0} is a power of 4",
                                        test_no);
        else
            Console.WriteLine("{0} is not a power of 4",
                                            test_no);
    }
}

// This code is contributed by mohit kumar 29

Javascript

<script>
// C++ program to check
// if given number is
// power of 4 or not


function isPowerOfFour( n)
{
    return n !=0 && ((n&(n-1)) == 0) && !(n & 0xAAAAAAAA);
}

/*Driver code*/
 test_no = 64;
    if(isPowerOfFour(test_no))
        document.write(test_no + " is a power of 4");
    else
        document.write(test_no + " is not a power of 4");
//This code is contributed by simranarora5sos
</script>

Output

64 is a power of 4

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

Method 5: A number will be a power of 4 if the floor(log4(num))=ceil(log4(num) because log4 of a number that is a power of 4 will always be an integer. 

Below is the implementation of the above approach. 

C++

// C++ program to check
// if given number is
// power of 4 or not
#include<bits/stdc++.h>

using namespace std;

float logn(int n, int r)
{
    return log(n) / log(r);
}

bool isPowerOfFour(int n)
{
    //0 is not considered as a power
    //of 4
    if(n == 0)
        return false;
    return floor(logn(n,4))==ceil(logn(n,4));
}

/*Driver code*/
int main()
{
    int test_no = 64;
    if(isPowerOfFour(test_no))
        cout << test_no << " is a power of 4" ;
    else
        cout << test_no << " is not a power of 4";
    return 0;
}

Java

// Java program to check
// if given number is
// power of 4 or not
import java.util.*;
class GFG{

static double logn(int n,
                   int r)
{
  return Math.log(n) /
         Math.log(r);
}

static boolean isPowerOfFour(int n)
{
  // 0 is not considered
  // as a power of 4
  if (n == 0)
    return false;
  return Math.floor(logn(n, 4)) ==
         Math.ceil(logn(n, 4));
}

// Driver code
public static void main(String[] args)
{
  int test_no = 64;
  if (isPowerOfFour(test_no))
    System.out.print(test_no +
                     " is a power of 4");
  else
    System.out.print(test_no +
                     " is not a power of 4");
}
}

// This code is contributed by Amit Katiyar

Python3

# Python3 program to check
# if given number is
# power of 4 or not
import math

def logn(n, r):
    return math.log(n) / math.log(r)

def isPowerOfFour(n):

    # 0 is not considered
    # as a power of 4
    if (n == 0):
        return False

    return (math.floor(logn(n, 4)) ==
             math.ceil(logn(n, 4)))

# Driver code
if __name__ == '__main__':

    test_no = 64

    if (isPowerOfFour(test_no)):
        print(test_no, " is a power of 4")
    else:
        print(test_no, " is not a power of 4")

# This code is contributed by Amit Katiyar

C#

// C# program to check
// if given number is
// power of 4 or not
using System;
class GFG{

static double logn(int n,
                   int r)
{
  return Math.Log(n) /
         Math.Log(r);
}

static bool isPowerOfFour(int n)
{
  // 0 is not considered
  // as a power of 4
  if (n == 0)
    return false;
  return Math.Floor(logn(n, 4)) ==
         Math.Ceiling(logn(n, 4));
}

// Driver code
public static void Main(String[] args)
{
  int test_no = 64;
  if (isPowerOfFour(test_no))
    Console.Write(test_no +
                  " is a power of 4");
  else
    Console.Write(test_no +
                  " is not a power of 4");
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// javascript program to check
// if given number is
// power of 4 or not


function logn( n,  r)
{
    return Math.log(n) / Math.log(r);
}

function isPowerOfFour( n)
{
    //0 is not considered as a power
    //of 4
    if(n == 0)
        return false;
    return Math.floor(logn(n,4))==Math.ceil(logn(n,4));
}

/*Driver code*/

    let test_no = 64;
    if(isPowerOfFour(test_no))
        document.write(test_no + " is a power of 4") ;
    else
        document.write( test_no + " is not a power of 4");

    // This code contributed by gauravrajput1

</script>

Output

64 is a power of 4

Time Complexity: O(log n)
Auxiliary Space: O(1)

Method 6: Using Log and without using ceil (Oneliner)

We can easily calculate without using ceil by checking the log of number base 4 to the power of 4 is equal to that number

C++

// C++ program to check
// if given number is
// power of 4 or not
#include <bits/stdc++.h>
using namespace std;

int isPowerOfFour(int n)
{
    return (n > 0 and pow(4, int(log2(n) /
                                 log2(4))) == n);
}

// Driver code
int main()
{
    int test_no = 64;

    if (isPowerOfFour(test_no))
        cout << test_no << " is a power of 4";
    else
        cout << test_no << " is not a power of 4";

    return 0;
}

// This code is contributed by ukasp

Java

// Java program to check
// if given number is
import java.io.*;

class GFG{

static boolean isPowerOfFour(int n)
{
    return (n > 0 && Math.pow(
        4, (int)((Math.log(n) /
                  Math.log(2)) /
                 (Math.log(4) /
                  Math.log(2)))) == n);
}

// Driver code
public static void main(String[] args)
{
    int test_no = 64;

    if (isPowerOfFour(test_no))
        System.out.println(test_no +
         " is a power of 4");
    else
        System.out.println(test_no +
         " is not a power of 4");
}
}

// This code is contributed by rag2127

Python3

# Python3 program to check
# if given number is
# power of 4 or not
import math


def isPowerOfFour(n):
    return (n > 0 and 4**int(math.log(n, 4)) == n)


# Driver code
if __name__ == '__main__':

    test_no = 64

    if (isPowerOfFour(test_no)):
        print(test_no, " is a power of 4")
    else:
        print(test_no, " is not a power of 4")

# This code is contributed by vikkycirus

C#

// C# program to check
// if given number is
using System;
class GFG
{

static Boolean isPowerOfFour(int n)
{
    return (n > 0 && Math.Pow(
        4, (int)((Math.Log(n) /
                  Math.Log(2)) /
                 (Math.Log(4) /
                  Math.Log(2)))) == n);
}

// Driver code
public static void Main(String[] args)
{
    int test_no = 64;

    if (isPowerOfFour(test_no))
        Console.WriteLine(test_no +
         " is a power of 4");
    else
        Console.WriteLine(test_no +
         " is not a power of 4");
}
}

// This code is contributed by shivanisinghss2110

Javascript

<script>

// Javascript program to check
// if given number is
// power of 4 or not
function isPowerOfFour(n)
{
    return (n > 0 && Math.pow(4, (Math.log2(n) /
                                 Math.log2(4)) == n));
}

// Driver code
let test_no = 64;

if (isPowerOfFour(test_no))
    document.write(test_no +
                   " is a power of 4");
else
    document.write(test_no +
                   " is not a power of 4");

// This code is contributed by avijitmondal1998

</script>

Output

64 is a power of 4

Time Complexity: O(log₄n)
Auxiliary Space: O(1)

Method 7: A number ‘n’ is a power of 4 if,

a) It is a perfect square
b) It is a power of two

Below is the implementation of the above idea.

C++

// C++ program to check if given number is power of 4 or not
#include <bits/stdc++.h>
using namespace std;

// Function to check perfect square
bool isPerfectSquare(int n)
{
    int x = sqrt(n);
    return (x * x == n);
}

bool isPowerOfFour(int n)
{
    // If n <= 0, it is not the power of four
    if (n <= 0)
        return false;
    // Check whether 'n' is a perfect square or not
    if (!isPerfectSquare(n))
        return false;

    // If 'n' is the perfect square Check for the second
    // condition i.e. 'n' must be power of two
    return !(n & (n - 1));
}

/*Driver code*/
int main()
{
    int test_no = 64;
    if (isPowerOfFour(test_no))
        cout << test_no << " is a power of 4";
    else
        cout << test_no << " is not a power of 4";
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

C

// C program to check if given number is power of 4 or not
#include <math.h>
#include <stdbool.h>
#include <stdio.h>

// Function to check perfect square
bool isPerfectSquare(int n)
{
    int x = sqrt(n);
    return (x * x == n);
}

bool isPowerOfFour(int n)
{
    // If n <= 0, it is not the power of four
    if (n <= 0)
        return false;
    // Check whether 'n' is a perfect square or not
    if (!isPerfectSquare(n))
        return false;

    // If 'n' is the perfect square Check for the second
    // condition i.e. 'n' must be power of two
    return !(n & (n - 1));
}

/*Driver code*/
int main()
{
    int test_no = 64;
    if (isPowerOfFour(test_no))
        printf("%d is a power of 4", test_no);
    else
        printf("%d is not a power of 4", test_no);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

Java

// Java program to check
// if given number is
// power of 4 or not
import java.util.*;

class GFG {

    // Function to check perfect square
    static boolean isPerfectSquare(int n) {
        int x = (int) Math.sqrt(n);

        return (x * x == n);
    }

    static boolean isPowerOfFour(int n)
    {

        // If n <= 0, it is not the power of four
        if (n <= 0)
            return false;

        // Check whether 'n' is a perfect square or not
        if (!isPerfectSquare(n))
            return false;

        // If 'n' is the perfect square
        // Check for the second condition i.e. 'n' must be power of two
        return (n & (n - 1)) != 1 ? true : false;
    }

    /* Driver code */
    public static void main(String[] args) {
        int test_no = 64;
        if (isPowerOfFour(test_no))
            System.out.print(test_no + " is a power of 4");
        else
            System.out.print(test_no + " is not a power of 4");
    }
}

// This code is contributed by gauravrajput1

Python3

# Python program to check
# if given number is
# power of 4 or not
# Function to check perfect square
# import the math module
import math

def isPerfectSquare(n):
    x = math.sqrt(n)
    return (x*x == n)


def isPowerOfFour(n):

      # If n <= 0, it is not the power of four
      if(n <= 0):
         return False

      # Check whether 'n' is a perfect square or not
      if(isPerfectSquare(n)):
         return False

      # If 'n' is the perfect square
      # Check for the second condition i.e. 'n' must be power of two
      return (n & (n - 1))

# Driver code
test_no = 64
if(isPowerOfFour(test_no)):
        print(test_no ," is a power of 4")
else:
        print(test_no ," is not a power of 4")

# This code is contributed by shivanisinghss2110

C#

// C# program to check
// if given number is
// power of 4 or not
using System;

public class GFG {

    // Function to check perfect square
    static bool isPerfectSquare(int n) {
        int x = (int) Math.Sqrt(n);

        return (x * x == n);
    }

    static bool isPowerOfFour(int n)
    {

        // If n <= 0, it is not the power of four
        if (n <= 0)
            return false;

        // Check whether 'n' is a perfect square or not
        if (!isPerfectSquare(n))
            return false;

        // If 'n' is the perfect square
        // Check for the second condition i.e. 'n' must be power of two
        return (n & (n - 1)) != 1 ? true : false;
    }

    /* Driver code */
    public static void Main(String[] args) {
        int test_no = 64;
        if (isPowerOfFour(test_no))
            Console.Write(test_no + " is a power of 4");
        else
            Console.Write(test_no + " is not a power of 4");
    }
}

// This code is contributed by umadevi9616

Javascript

<script>

// JavaScript program to check
// if given number is
// power of 4 or not
// Function to check perfect square
function isPerfectSquare( n) {
        var x = Math.sqrt(n);

        return (x * x == n);
    }

function isPowerOfFour(n)
    {

        // If n <= 0, it is not the power of four
        if (n <= 0)
            return false;

        // Check whether 'n' is a perfect square or not
        if (!isPerfectSquare(n))
            return false;

        // If 'n' is the perfect square
        // Check for the second condition i.e. 'n' must be power of two
        return (n & (n - 1)) != 1 ? true : false;
    }

    /* Driver code */
        var test_no = 64;
        if (isPowerOfFour(test_no))
            document.write(test_no + " is a power of 4");
        else
            document.write(test_no + " is not a power of 4");

// This code is contributed by shivanisinghss2110

</script>

Output

64 is a power of 4

Time Complexity: O(log₂n)
Auxiliary Space: O(1)

Method 8: Using a similar concept of “Power of 2”:

A number can be considered a power of 4 when:

1. * The number is a power of 2 for example : 4, 16, 64 … all are powers of 2 as well . The O(1) bit manipulation technique using n&(n-1)==0 can be used, but wait every power of 4 is a power of 2. Will the reverse apply?
2. *Obviously not, 8,32,128 … aren’t power of 4, so we need one more check here. If you clearly notice all powers of 4 when divided by 3 gives 1 as the remainder.

Below is the code implementation of the above approach:

C++

#include <bits/stdc++.h>
using namespace std;

// C++ code to check if given
// number is power of 4 or not

// Function to check if
// x is power of 4
bool isPowerOfFour(int n)
{
  return ((n > 0) && ((n & n - 1) == 0) && (n % 3 == 1));
}

// Driver program
int main()
{
  int test_no = 64;
  if (isPowerOfFour(test_no) == true)
    cout << (test_no) << " is a power of 4";
  else
    cout << (test_no) << " is not a power of 4";
}

// This code is contributed by garg28harsh.

Java

/*package whatever //do not write package name here */

import java.io.*;

// Java code to check if given
// number is power of 4 or not

class GFG {

    // Function to check if
    // x is power of 4
    static boolean isPowerOfFour(int n)
    {
        return ((n>0) && ((n & n-1) == 0) && (n%3 == 1));
    }

    // Driver program
    public static void main(String[] args)
    {
        int test_no = 64;
        if(isPowerOfFour(test_no) == true)
        System.out.println(test_no +
                        " is a power of 4");
        else
        System.out.println(test_no +
                        " is not a power of 4");
    }
}

// This code is contributed
// Aravind Ravi

Python3

# Python code to check if given
# number is power of 4 or not

# Function to check if
# x is power of 4

def isPowerOfFour(n):

    return ((n > 0) and ((n & n - 1) == 0) and (n % 3 == 1))

# Driver code
test_no = 64
if(isPowerOfFour(test_no)):
        print(test_no,"is a power of 4")
else:
        print(test_no,"is not a power of 4")

# This code is contributed by Pushpesh Raj.

C#

using System;

// C# code to check if given
// number is power of 4 or not
class GFG
{

  // Function to check if
  // x is power of 4
  static bool isPowerOfFour(int n)
  {
    return ((n > 0) && ((n & n - 1) == 0)
            && (n % 3 == 1));
  }
  static void Main()
  {
    int test_no = 64;
    if (isPowerOfFour(test_no) == true)
      Console.Write(test_no + " is a power of 4");
    else
      Console.Write(test_no + " is not a power of 4");
  }
}

// This code is contributed by garg28harsh.

Javascript

// JavaScript code to check if given
// number is power of 4 or not

function isPowerOfFour(n){
    return ((n>0) && ((n & n-1) == 0) && (n%3 == 1));
}

let test_no = 64
if(isPowerOfFour(test_no)==true){
    console.log(test_no + " is a power of 4");
}
else{
    console.log(test_no + " is not a power of 4");
}

// This code is contributed lokeshmvs21.

Output

64 is a power of 4

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

Method 9: Alternative approach: Using built-in methods (one-liner)

Any number that is a power of 4 has the following properties:

1. It is a power of 2 (that is, only its leftmost bit is set)
2. It has an even number of unset bits.

Most languages have in-built methods to count the number of leading and trailing unset bits, such as __builtin_clz in C++,  numberOfLeadingZeros() in Java, and bit_length() in Python3. If a number is a power of 2, then it shall only have one set bit. Therefore, if the number of trailing zeros is even, then it is a power of 4.

The approach is shown below:

C++

// C++ program to check if given number is power of 4 or not
#include <bits/stdc++.h>
using namespace std;

bool isPowerOfFour(int n)
{
    return !(n & (n - 1)) && ((32 - __builtin_clz(n)) % 2);
}

/*Driver code*/
int main()
{
    int test_no = 64;
    if (isPowerOfFour(test_no))
        cout << test_no << " is a power of 4\n";

    else
        cout << test_no << " is not a power of 4\n";

    return 0;
}

// This code is contributed by phasing17

Java

// Java program to check if given number is power of 4 or not
import java.util.*;

public class GFG
{
  static boolean isPowerOfFour(int n)
  {
    return ((n & (n - 1)) == 0) && ((32 -  Integer.numberOfLeadingZeros(n)) % 2 != 0);
  }

  /*Driver code*/
  public static void main(String[] args)
  {
    int test_no = 64;
    if (isPowerOfFour(test_no))
      System.out.println(test_no + " is a power of 4\n");

    else
      System.out.println(test_no + " is not a power of 4\n");

  }
}

// This code is contributed by phasing17

Python3

# Python code for the above approach
import math

def isPowerOfFour(n):
    return ((n & (n-1)) == 0) and ((32 + 1 - (math.floor(math.log(n)/math.log(2)))) % 2 == 1)

test_no = 64
if(isPowerOfFour(test_no)):
    print(test_no, "is a power of 4")
else:
    print(test_no, "is not a power of 4")

# This code is contributed by lokeshmvs21.

C#

// C# program to check if given number is power of 4 or not
using System;
using System.Collections.Generic;

public class GFG
{
  static bool isPowerOfFour(int n)
  {
    return ((n & (n - 1)) == 0) && ((32 + 1 - (Math.Floor(Math.Log(n) / Math.Log(2)))) % 2 == 1);
  }

  /*Driver code*/
  public static void Main(string[] args)
  {
    int test_no = 64;
    if (isPowerOfFour(test_no))
      Console.WriteLine(test_no + " is a power of 4\n");

    else
      Console.WriteLine(test_no + " is not a power of 4\n");
  }
}

// This code is contributed by phasing17

Javascript

// JS program to check if given number is power of 4 or not

function isPowerOfFour(n)
{
    return !(n & (n - 1)) && (32 + 1 - (Math.floor(Math.log(n) / Math.log(2)))) % 2;
}

/*Driver code*/
let test_no = 64;
if (isPowerOfFour(test_no))
    console.log(test_no + " is a power of 4");
else
    console.log(test_no + " is not a power of 4");


// This code is contributed by phasing17

Output

64 is a power of 4

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

Method 10: Using math module and is_integer 

1. This function takes an integer n as input and returns True if it is a power of 4 and False otherwise. 

2. The math.log function is used to calculate the logarithm base 4 of n. 

3. The is_integer method is used to check if the result is an integer.

C++

#include <iostream>
#include <cmath>
using namespace std;

bool is_power_of_4_log(int n) {
    if (n <= 0) {
        return false;
    }
    return fmod(log(n) / log(4), 1) == 0;
}

int main() {
    cout << is_power_of_4_log(16) << endl;
    cout << is_power_of_4_log(36) << endl;
    cout << is_power_of_4_log(20) << endl;
    return 0;
}

Python3

import math

def is_power_of_4_log(n):
    if n <= 0:
        return False
    return math.log(n, 4).is_integer()
print(is_power_of_4_log(16))
print(is_power_of_4_log(36))
print(is_power_of_4_log(20))

C#

using System;

class Program
{

  // This function checks if a number is a power of 4
  // using logarithms.
  static bool IsPowerOf4Log(int n)
  {

    // If n is less than or equal to 0, it cannot be a
    // power of 4.
    if (n <= 0) {
      return false;
    }
    // Check if the logarithm of n to base 4 is an
    // integer.
    return Math.IEEERemainder(Math.Log(n) / Math.Log(4),
                              1)
      == 0;
  }

  static void Main(string[] args)
  {

    Console.WriteLine(IsPowerOf4Log(16));
    Console.WriteLine(IsPowerOf4Log(36));
    Console.WriteLine(IsPowerOf4Log(20));
  }
}

Javascript

function is_power_of_4_log(n) {
    if (n <= 0) {
        return false;
    }
    return Number.isInteger(Math.log(n) / Math.log(4));
}

console.log(is_power_of_4_log(16)==1?"True":"False");
console.log(is_power_of_4_log(36)==1?"True":"False");
console.log(is_power_of_4_log(20)==1?"True":"False");

Java

public class Main {
    public static void main(String[] args) {
        System.out.println(isPowerOf4Log(16)); // true
        System.out.println(isPowerOf4Log(36)); // false
        System.out.println(isPowerOf4Log(20)); // false
    }

    public static boolean isPowerOf4Log(int n) {
        if (n <= 0) {
            return false;
        }
        return (Math.log(n) / Math.log(4)) % 1 == 0;
    }
}

Output

True
False
False

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

Please write comments if you find any of the above codes/algorithms incorrect, or find other ways to solve the same problem