Ugly Number

An ugly number is positive and has no prime factors other than 2, 3, and 5. Repeatedly divide n by 2 while divisible, then by 3, then by 5. If the remaining value is one, every prime factor was allowed; otherwise a disallowed prime factor remains. This is simpler and safer than testing every factor up to square root. The number of divisions is logarithmic in n, so time is O(log n) and extra space is O(1). Explicitly handle n less than or equal to zero as false, and n=1 as true because it has no disallowed prime factors. Use integer division only after modulo confirms divisibility. Test primes like 7, powers of an allowed factor, mixed allowed factors, and values with one disallowed factor such as 14.