Ugly Number

LeetCode 263 | Difficulty: Easy

Easy

Problem Description

An ugly number is a positive integer which does not have a prime factor other than 2, 3, and 5.

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

Example 1:

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

Example 2:

Input: n = 1
Output: true
Explanation: 1 has no prime factors.

Example 3:

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

Constraints:

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

Topics: Math

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Approach

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

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Solutions

Solution 1: C# (Best: 52 ms)

Metric	Value
Runtime	52 ms
Memory	N/A
Date	2018-04-12

Solution

public class Solution {
    public bool IsUgly(int num) {
        if(num==1) return true;
    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;
    }
}

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Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.