19728 has 30 divisors (see below), whose sum is σ = 55614. Its totient is φ = 6528.

The previous prime is 19727. The next prime is 19739. The reversal of 19728 is 82791.

It can be written as a sum of positive squares in only one way, i.e., 17424 + 2304 = 132^2 + 48^2 .

It is a nialpdrome in base 12.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (19727) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 76 + ... + 212.

2¹⁹⁷²⁸ is an apocalyptic number.

19728 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 19728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (27807).

19728 is an abundant number, since it is smaller than the sum of its proper divisors (35886).

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

19728 is a wasteful number, since it uses less digits than its factorization.

19728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 151 (or 142 counting only the distinct ones).

The product of its digits is 1008, while the sum is 27.

The square root of 19728 is about 140.4563989286. The cubic root of 19728 is about 27.0205604709.

Subtracting from 19728 its sum of digits (27), we obtain a triangular number (19701 = T₁₉₈).

Adding to 19728 its product of digits (1008), we get a 4-th power (20736 = 12⁴).

It can be divided in two parts, 197 and 28, that added together give a square (225 = 15²).

The spelling of 19728 in words is "nineteen thousand, seven hundred twenty-eight".