# Check if number is power of 3

Determining whether a given number is a power of 3 or not is an interesting mathematical problem. In this scenario, we want to identify whether a given integer can be expressed as 3 raised to some positive integer exponent. This problem has real-world applications in various fields including computer science, physics, and engineering. It's particularly relevant in cases where computations involving powers of 3 are required, like in algorithms or calculations involving ternary systems.

## Problem Statement and Description

The problem can be framed as follows: Given an integer `number`

, we need to determine whether it can be
expressed in the form `3^k`

where `k`

is a positive integer. In other words, we need to
identify if `number`

is a power of 3.

For instance, if we take the number 81, it can be expressed as `3^4`

which is indeed a power of 3. On the
other hand, the number 18 cannot be expressed in such a form. Similarly, 27 is `3^3`

, making it a power
of 3, while 30 is not.

## Idea to Solve the Problem

One way to approach this problem is to leverage the fact that powers of 3 have a distinct property: they are divisors
of a very large power of 3. The highest power of 3 that can fit into a 32-bit unsigned integer is 3486784401
(`3^20`

). If a number is a power of 3, it must be a divisor of this highest power of 3 without leaving a
remainder.

## Pseudocode and Algorithm

```
Function isPowerOfThree(number):
if 3486784401 % number == 0:
print "Number", number, "is a power of 3"
else:
print "Number", number, "is not a power of 3"
```

## Explanation of Algorithm

- For each number in the main function, the
`isPowerOfThree`

function is called. - Inside
`isPowerOfThree`

function, it checks whether the given`number`

divides 3486784401 (highest power of 3 that fits in a 32-bit unsigned integer) evenly, i.e., without leaving a remainder. - If the condition is satisfied, the function prints that the number is a power of 3; otherwise, it prints that the number is not a power of 3.

## Code Solution

```
// C program for
// Check if number is power of 3
#include <stdio.h>
// Check if that given number is power of 3 or not
void isPowerOfThree(int number)
{
if (3486784401u % number == 0)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
printf(" Number %d is power of 3 \n", number);
}
else
{
printf(" Number %d is not power of 3 \n", number);
}
}
int main(int argc, char const *argv[])
{
// Test Case
isPowerOfThree(81);
isPowerOfThree(18);
isPowerOfThree(27);
isPowerOfThree(30);
isPowerOfThree(-27);
return 0;
}
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number -27 is not power of 3
```

```
/*
Java Program for
Check if number is power of 3
*/
public class Power
{
// Check whether given number is power of 3 or not
public void isPowerOfThree(long number)
{
if (3486784401L % number == 0)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
System.out.println(" Number " + number + " is power of 3 ");
}
else
{
System.out.println(" Number " + number + " is not power of 3 ");
}
}
public static void main(String[] args)
{
Power task = new Power();
// Test Case
task.isPowerOfThree(81);
task.isPowerOfThree(18);
task.isPowerOfThree(27);
task.isPowerOfThree(30);
// 3 ^ 0 = 1
task.isPowerOfThree(1);
task.isPowerOfThree(-27);
}
}
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
// Include header file
#include <iostream>
using namespace std;
/*
C++ Program for
Check if number is power of 3
*/
class Power
{
public:
// Check whether given number is power of 3 or not
void isPowerOfThree(long number)
{
if (3486784401L % number == 0)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
cout << " Number " << number << " is power of 3 " << endl;
}
else
{
cout << " Number " << number << " is not power of 3 " << endl;
}
}
};
int main()
{
Power *task = new Power();
// Test Case
task->isPowerOfThree(81);
task->isPowerOfThree(18);
task->isPowerOfThree(27);
task->isPowerOfThree(30);
// 3 ^ 0 = 1
task->isPowerOfThree(1);
task->isPowerOfThree(-27);
return 0;
}
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
// Include namespace system
using System;
/*
Csharp Program for
Check if number is power of 3
*/
public class Power
{
// Check whether given number is power of 3 or not
public void isPowerOfThree(long number)
{
if (3486784401L % number == 0)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
Console.WriteLine(" Number " + number + " is power of 3 ");
}
else
{
Console.WriteLine(" Number " + number + " is not power of 3 ");
}
}
public static void Main(String[] args)
{
Power task = new Power();
// Test Case
task.isPowerOfThree(81);
task.isPowerOfThree(18);
task.isPowerOfThree(27);
task.isPowerOfThree(30);
// 3 ^ 0 = 1
task.isPowerOfThree(1);
task.isPowerOfThree(-27);
}
}
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
<?php
/*
Php Program for
Check if number is power of 3
*/
class Power
{
// Check whether given number is power of 3 or not
public function isPowerOfThree($number)
{
if (3486784401 % $number == 0)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
echo " Number ".$number.
" is power of 3 ".
"\n";
}
else
{
echo " Number ".$number.
" is not power of 3 ".
"\n";
}
}
}
function main()
{
$task = new Power();
// Test Case
$task->isPowerOfThree(81);
$task->isPowerOfThree(18);
$task->isPowerOfThree(27);
$task->isPowerOfThree(30);
// 3 ^ 0 = 1
$task->isPowerOfThree(1);
$task->isPowerOfThree(-27);
}
main();
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
/*
Node JS Program for
Check if number is power of 3
*/
class Power
{
// Check whether given number is power of 3 or not
isPowerOfThree(number)
{
if (3486784401 % number == 0)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
console.log(" Number " + number + " is power of 3 ");
}
else
{
console.log(" Number " + number + " is not power of 3 ");
}
}
}
function main()
{
var task = new Power();
// Test Case
task.isPowerOfThree(81);
task.isPowerOfThree(18);
task.isPowerOfThree(27);
task.isPowerOfThree(30);
// 3 ^ 0 = 1
task.isPowerOfThree(1);
task.isPowerOfThree(-27);
}
main();
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
# Python 3 Program for
# Check if number is power of 3
class Power :
# Check whether given number is power of 3 or not
def isPowerOfThree(self, number) :
if (3486784401 % number == 0) :
# Highest power of 3 in unsigned integer
# 3486784401 (3^20)
# That is divisible by 3 and remainder is zero
print(" Number", number ," is power of 3 ")
else :
print(" Number", number ," is not power of 3 ")
def main() :
task = Power()
# Test Case
task.isPowerOfThree(81)
task.isPowerOfThree(18)
task.isPowerOfThree(27)
task.isPowerOfThree(30)
# 3 ^ 0 = 1
task.isPowerOfThree(1)
task.isPowerOfThree(-27)
if __name__ == "__main__": main()
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
# Ruby Program for
# Check if number is power of 3
class Power
# Check whether given number is power of 3 or not
def isPowerOfThree(number)
if (3486784401 % number == 0)
# Highest power of 3 in unsigned integer
# 3486784401 (3^20)
# That is divisible by 3 and remainder is zero
print(" Number ", number ," is power of 3 ", "\n")
else
print(" Number ", number ," is not power of 3 ", "\n")
end
end
end
def main()
task = Power.new()
# Test Case
task.isPowerOfThree(81)
task.isPowerOfThree(18)
task.isPowerOfThree(27)
task.isPowerOfThree(30)
# 3 ^ 0 = 1
task.isPowerOfThree(1)
task.isPowerOfThree(-27)
end
main()
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
/*
Scala Program for
Check if number is power of 3
*/
class Power()
{
// Check whether given number is power of 3 or not
def isPowerOfThree(number: Long): Unit = {
if (3486784401L % number == 0)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
println(" Number " + number + " is power of 3 ");
}
else
{
println(" Number " + number + " is not power of 3 ");
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Power = new Power();
// Test Case
task.isPowerOfThree(81);
task.isPowerOfThree(18);
task.isPowerOfThree(27);
task.isPowerOfThree(30);
// 3 ^ 0 = 1
task.isPowerOfThree(1);
task.isPowerOfThree(-27);
}
}
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
/*
Swift 4 Program for
Check if number is power of 3
*/
class Power
{
// Check whether given number is power of 3 or not
func isPowerOfThree(_ number: Int)
{
if (3486784401 % number == 0)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
print(" Number ", number ," is power of 3 ");
}
else
{
print(" Number ", number ," is not power of 3 ");
}
}
}
func main()
{
let task: Power = Power();
// Test Case
task.isPowerOfThree(81);
task.isPowerOfThree(18);
task.isPowerOfThree(27);
task.isPowerOfThree(30);
// 3 ^ 0 = 1
task.isPowerOfThree(1);
task.isPowerOfThree(-27);
}
main();
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

```
/*
Kotlin Program for
Check if number is power of 3
*/
class Power
{
// Check whether given number is power of 3 or not
fun isPowerOfThree(number: Long): Unit
{
if ((3486784401 % number) == 0L)
{
/*
Highest power of 3 in unsigned integer
3486784401 (3^20)
That is divisible by 3 and remainder is zero
*/
println(" Number " + number + " is power of 3 ");
}
else
{
println(" Number " + number + " is not power of 3 ");
}
}
}
fun main(args: Array < String > ): Unit
{
val task: Power = Power();
// Test Case
task.isPowerOfThree(81);
task.isPowerOfThree(18);
task.isPowerOfThree(27);
task.isPowerOfThree(30);
// 3 ^ 0 = 1
task.isPowerOfThree(1);
task.isPowerOfThree(-27);
}
```

#### input

```
Number 81 is power of 3
Number 18 is not power of 3
Number 27 is power of 3
Number 30 is not power of 3
Number 1 is power of 3
Number -27 is power of 3
```

## Time Complexity

The time complexity of this algorithm is O(1), which means it takes a constant amount of time regardless of the input
size. This is because the modulo operation (`%`

) and the division operation are both constant time
operations.

## Another Solution

```
import math
def is_power_of_three(n):
if n <= 0:
return False
else:
return math.log10(n)/math.log10(3) % 1 == 0
# Example usage:
print(is_power_of_three(9)) # True
print(is_power_of_three(27)) # True
print(is_power_of_three(10)) # False
```

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