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.

1. A simple method is to take log of the given number on base 4, and if we get an integer then number is power of 4.

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 
?> 

Output :

64 is a power of 4

3. A number n is a power of 4 if 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 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 contribued 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 
?> 

Output:

64 is a power of 4

4. A number n is a power of 4 if 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"); 
    } 
} 

Output:

64 is a power of 4

Why 0xAAAAAAAA ? This is because the bit representation is of powers of 2 that are not of 4. Like 2, 8, 32 so on..
Please write comments if you find any of the above codes/algorithms incorrect, or find other ways to solve the same problem.

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