# 342 Power of Four

## Problem Statement

Given an integer `n`

, return * true if it is a power of four. Otherwise, return false*.

An integer

`n`

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

such that `n == 4x`

.**Input:** n = 16

**Output:** true

**Input:** n = 5

**Output:** false

**Input:** n = 1

**Output:** true

## Approach

We can solve this with Recursion where we recursively call the function with `n = n / 4`

.

The base case has to be defined as `n === 1`

. If we reach 1 we know that the passed in number is a power of four.

To get to the base case we have to understand exponents. If the integer `n`

is equal to `1`

it can be expressed as `4^0`

, which satisfies the definition of a power of four and is the smallest possible case of power of four.

## Solution

```
var isPowerOfFour = function(n) {
if (n === 1) return true
if (n < 1) return false
return isPowerOfFour(n / 4)
};
```