# Question

Formatted question description: https://leetcode.ca/all/326.html

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 == 3x.

Example 1:

Input: n = 27
Output: true
Explanation: 27 = 33


Example 2:

Input: n = 0
Output: false
Explanation: There is no x where 3x = 0.


Example 3:

Input: n = -1
Output: false
Explanation: There is no x where 3x = (-1).


Constraints:

• -231 <= n <= 231 - 1

Follow up: Could you solve it without loops/recursion?

# Algorithm

The most straightforward way is to keep dividing by 3 to see if the final iterative quotient is 1. Pay attention to the case where the input is negative and 0.

If no loop, there is a tricky method. Since the input is an int, the range of positive numbers is 0 - 2^31, and the largest power of 3 allowed in this range is 3^19=1162261467, so we only need to see if this number is divisible by n.

# Code

• 
public class Power_of_Three {

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

public class Solution {
public boolean isPowerOfThree(int n) {
if (n < 1) {
return false;
}

while (n % 3 == 0) {
n /= 3;
}

return n == 1;
}
}
}

############

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

• // OJ: https://leetcode.com/problems/power-of-three/
// Time: O(log3(N))
// Space: O(1)
class Solution {
public:
bool isPowerOfThree(int n) {
if (n < 1) return false;
while (n % 3 == 0) n /= 3;
return n == 1;
}
};

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

############

class Solution(object):
def isPowerOfThree(self, n):
"""
:type n: int
:rtype: bool
"""
if n > 0:
return (1162261467 % n) == 0
else:
return False


• func isPowerOfThree(n int) bool {
return n > 0 && 1162261467%n == 0
}

• function isPowerOfThree(n: number): boolean {
return n > 0 && 1162261467 % n == 0;
}


• /**
* @param {number} n
* @return {boolean}
*/
var isPowerOfThree = function (n) {
return n > 0 && 1162261467 % n == 0;
};