199728 has 60 divisors (see below), whose sum is σ = 596440. Its totient is φ = 62208.

The previous prime is 199721. The next prime is 199729. The reversal of 199728 is 827991.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (36).

199728 is an undulating number in base 8.

It is a nialpdrome in base 12.

It is a zygodrome in base 2.

It is a junction number, because it is equal to n+sod(n) for n = 199692 and 199701.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (199721) by changing a digit.

199728 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2700 + ... + 2772.

2¹⁹⁹⁷²⁸ is an apocalyptic number.

199728 is a gapful number since it is divisible by the number (18) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 199728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (298220).

199728 is an abundant number, since it is smaller than the sum of its proper divisors (396712).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

199728 is a wasteful number, since it uses less digits than its factorization.

199728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 106 (or 97 counting only the distinct ones).

The product of its digits is 9072, while the sum is 36.

The square root of 199728 is about 446.9093867889. The cubic root of 199728 is about 58.4538316426.

It can be divided in two parts, 1997 and 28, that added together give a square (2025 = 45²).

The spelling of 199728 in words is "one hundred ninety-nine thousand, seven hundred twenty-eight".