*This is part of a series of Leetcode solution explanations (index). If you liked this solution or found it useful,* *please like**this post and/or* *upvote**my solution post on Leetcode's forums.*

####
Leetcode Problem #326 (*Easy*): Power of Three

####
*Description:*

*Description:*

(*Jump to*: *Solution Idea* || *Code*: *JavaScript* | *Python* | *Java* | *C++*)

Given an integer

`n`

, return`true`

if it is a power of three. Otherwise, return`false`

.An integer

`n`

is a power of three, if there exists an integer`x`

such that`n == 3^x`

.

Follow up: Could you solve itwithoutloops/recursion?

####
*Examples:*

*Examples:*

Example 1: Input: n = 27 Output: true

Example 2: Input: n = 0 Output: false

Example 3: Input: n = 9 Output: true

Example 4: Input: n = 45 Output: false

####
*Constraints:*

*Constraints:*

`-2^31 <= n <= 2^31 - 1`

####
*Idea:*

*Idea:*

(*Jump to*: *Problem Description* || *Code*: *JavaScript* | *Python* | *Java* | *C++*)

The naive approach here would be to simply iterate through dividing **n** by **3** to see if we ultimately get to **1**. But if we want to accomplish this solution *without* iteration or recursion, we'll have to get creative.

**Approach 1: Logarithms -**

We can take advantage of the natural mathematical properties of **logarithms** to find our solution. If **n** is a power of **3**, then **3^x = n**. This can be rewritten as **log3 n = x**, where **x** will be an integer if **n** is a power of **3**.

Since most programming languages can't natively do **log3** calculations, we can take advantage of another property of logarithms: **log3 n** can be rewritten as **log n / log 3**. This will produce a slight amount of floating point error, but any value that is within a close margin (**1e-10**) while **n** is constrained to an **int** will be a correct.

**Approach 2: Modulo -**

Since **3** is a prime number, any power of **3** will only be divisible by any power of **3** that is equal or smaller. We can use this to our advantage by taking the largest possible power of **3** within our constraints (**3^19**) and performing a **modulo** **n** operation on it. If the result is a **0**, then **n** is a power of **3**.

####
*Javascript Code:*

*Javascript Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

#####
*w/ Logarithms:*

*w/ Logarithms:*

```
var isPowerOfThree = function(n) {
let a = Math.log(n) / Math.log(3)
return Math.abs(a - Math.round(a)) < 1e-10
};
```

#####
*w/ Modulo:*

*w/ Modulo:*

```
var isPowerOfThree = function(n) {
return n > 0 && 1162261467 % n === 0
};
```

####
*Python Code:*

*Python Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

#####
*w/ Logarithms:*

*w/ Logarithms:*

```
class Solution:
def isPowerOfThree(self, n: int) -> bool:
if n < 1: return False
ans = log(n, 3)
return abs(ans - round(ans)) < 1e-10
```

#####
*w/ Modulo:*

*w/ Modulo:*

```
class Solution:
def isPowerOfThree(self, n: int) -> bool:
return n > 0 and 1162261467 % n == 0
```

####
*Java Code:*

*Java Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

#####
*w/ Logarithms:*

*w/ Logarithms:*

```
class Solution {
public boolean isPowerOfThree(int n) {
double a = Math.log(n) / Math.log(3);
return Math.abs(a - Math.round(a)) < 1e-10;
}
}
```

#####
*w/ Modulo:*

*w/ Modulo:*

```
class Solution {
public boolean isPowerOfThree(int n) {
return n > 0 && 1162261467 % n == 0;
}
}
```

####
*C++ Code:*

*C++ Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

#####
*w/ Logarithms:*

*w/ Logarithms:*

```
class Solution {
public:
bool isPowerOfThree(int n) {
double a = log(n) / log(3);
return abs(a - round(a)) < 1e-10;
}
};
```

#####
*w/ Modulo:*

*w/ Modulo:*

```
class Solution {
public:
bool isPowerOfThree(int n) {
return n > 0 && 1162261467 % n == 0;
}
};
```

## Top comments (1)

Here is my attempt on this problem :

Leetcode Daily Challenge + Other resources