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

題意：給定一個數字，判斷是否為ugly number；其定義是：

• 是一個正整數
• 其素數因式分解中，僅能包含素數2，3或5

解法：首先，根據第一個要求我們可以排除掉小於1的所有數都不是ugly number；對於1來說雖然沒有素數的因式分解，但其是一個ugly number；最後，我們只需要計算是否滿足第二個條件即可，可以將其進行素數的因式分解；

Java

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