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.

Example 1:

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

Example 2:

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

Example 3:

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

Note:

1. 1 is typically treated as an ugly number.
2. Input is within the 32-bit signed integer range: [−231,  231 − 1].

这道题让我们检测一个数是否为丑陋数，所谓丑陋数就是其质数因子只能是 2，3，5。那么最直接的办法就是不停的除以这些质数，如果剩余的数字是1的话就是丑陋数了，参见代码如下：

解法一：

class Solution {
public:
    bool isUgly(int num) {
        while (num >= 2) {
            if (num % 2 == 0) num /= 2;
            else if (num % 3 == 0) num /= 3;
            else if (num % 5 == 0) num /= 5;
            else return false;
        }
        return num == 1;
    }
};

我们也可以换一种写法，分别不停的除以 2，3，5，并且看最后剩下来的数字是否为1即可，参见代码如下：

解法二：

class Solution {
public:
    bool isUgly(int num) {
        if (num <= 0) return false;
        while (num % 2 == 0) num /= 2;
        while (num % 3 == 0) num /= 3;
        while (num % 5 == 0) num /= 5;
        return num == 1;
    }
};

Github 同步地址：

#263

类似题目：

Super Ugly Number

Ugly Number II

Happy Number

Count Primes

参考资料：

https://leetcode.com/problems/ugly-number/

https://leetcode.com/problems/ugly-number/discuss/69225/My-2ms-java-solution

https://leetcode.com/problems/ugly-number/discuss/69214/2-4-lines-every-language

https://leetcode.com/problems/ugly-number/discuss/69332/Simple-java-solution-with-explanation

https://leetcode.com/problems/ugly-number/discuss/69308/Java-solution-greatest-divide-by-2-3-5

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