# 263. Ugly Number

## LeetCode [263. Ugly Number](https://github.com/txfs19260817/LeetCode-Go/blob/master/solutions/title/README.md)

### Description

Given an integer `n`, return `true` *if* `n` *is an **ugly number***.

**Ugly number** is a positive number whose prime factors only include `2`, `3`, and/or `5`.

**Example 1:**

```
Input: n = 6
Output: true
Explanation: 6 = 2 × 3
```

**Example 2:**

```
Input: n = 8
Output: true
Explanation: 8 = 2 × 2 × 2
```

**Example 3:**

```
Input: n = 14
Output: false
Explanation: 14 is not ugly since it includes another prime factor 7.
```

**Constraints:**

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

### Tags

Math

### Solution

If the input number is a non-positive number then return false immediately. We keep dividing this number by 2, 3, 5 until the number is equal to 1 (true) or is not divisible by them (false).

### Complexity

* Time complexity: $$O(\log(n))$$, we repeatly divide the given number by 2 or higher;
* Space complexity: $$O(1)$$

### Code

```go
func isUgly(n int) bool {
	if n <= 0 {
		return false
	}
	for n != 1 {
		switch {
		case n%2 == 0:
			n /= 2
		case n%3 == 0:
			n /= 3
		case n%5 == 0:
			n /= 5
		default:
			return false
		}
	}
	return true
}
```