30816 has 36 divisors (see below), whose sum is σ = 88452. Its totient is φ = 10176.

The previous prime is 30809. The next prime is 30817. The reversal of 30816 is 61803.

It is a tau number, because it is divible by the number of its divisors (36).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 14.

It is a zygodrome in base 2.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 30816.

It is not an unprimeable number, because it can be changed into a prime (30817) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 235 + ... + 341.

It is an arithmetic number, because the mean of its divisors is an integer number (2457).

2³⁰⁸¹⁶ is an apocalyptic number.

30816 is a gapful number since it is divisible by the number (36) 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 30816, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (44226).

30816 is an abundant number, since it is smaller than the sum of its proper divisors (57636).

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

30816 is a wasteful number, since it uses less digits than its factorization.

30816 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 123 (or 112 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 30816 is about 175.5448660599. The cubic root of 30816 is about 31.3515311020.

It can be divided in two parts, 308 and 16, that added together give a square (324 = 18²).

The spelling of 30816 in words is "thirty thousand, eight hundred sixteen".