> For the complete documentation index, see [llms.txt](https://aaronice.gitbook.io/lintcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://aaronice.gitbook.io/lintcode/mathematics/ugly_number.md).

# Ugly Number

## Question

Write a program to check whether a given number is an `ugly number`.

Ugly numbers are positive numbers whose prime factors only include 2, 3, 5. For example, 6, 8 are ugly while 14 is not ugly since it includes another prime factor 7.

**Notice**

Note that 1 is typically treated as an ugly number.

**Example**

Given num = 8 return true\
Given num = 14 return false

## Analysis

基本思路就是，对于num，如果取余数（2，3，5中其一）为0，说明对应的prime number能够被整除，所以一直除下去。最终如果是Ugly Number，该结果应当是1。时间复杂度是O(logn)。

## Solution

```java
public class Solution {
    /**
     * @param num an integer
     * @return true if num is an ugly number or false
     */
    public boolean isUgly(int num) {
        if (num == 0) {
            return false;
        }
        if (num == 1) {
            return true;
        }
        int[] primes = new int[]{2, 3, 5};
        for (int i = 0; i < primes.length; i++) {
            while (num % primes[i] == 0) {
                num = num / primes[i];
            }
        }
        return num == 1;
    }
}
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://aaronice.gitbook.io/lintcode/mathematics/ugly_number.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.