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This approach involves dividing the number by its prime factors (2, 3, and 5) as long as it is divisible by them. If after removing all these factors, the number reduces to 1, it is an ugly number; otherwise, it is not.
Time Complexity: O(log n).
Space Complexity: O(1).
1public class Solution {
2 public boolean isUgly(int n) {
3 if (n <= 0) return false;
4 int[] primes = {2, 3, 5};
5 for (int p : primes) {
6 while (n % p == 0) {
7 n /= p;
8 }
9 }
10 return n == 1;
11 }
12}This Java solution uses integer division within a loop to strip n of its prime factors (2, 3, 5). If n equals 1 by the end, it is an ugly number.
This alternative approach involves using recursion to systematically divide the number by 2, 3, and 5. By tracing back all divisions reaching 1, this method can also verify the ugliness of a number.
Time Complexity: O(log n).
Space Complexity: O(log n), due to recursion stack.
1def is_uglyIn this Python implementation, a nested helper function utilizes recursion to check each prime factor condition, ultimately confirming whether 1 is reached.