102816 has 96 divisors (see below), whose sum is σ = 362880. Its totient is φ = 27648.

The previous prime is 102811. The next prime is 102829. The reversal of 102816 is 618201.

It is a tau number, because it is divible by the number of its divisors (96).

It is a super-2 number, since 2×102816² = 21142259712, which contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (102811) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 6040 + ... + 6056.

It is an arithmetic number, because the mean of its divisors is an integer number (3780).

2¹⁰²⁸¹⁶ is an apocalyptic number.

102816 is a gapful number since it is divisible by the number (16) 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 102816, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (181440).

102816 is an abundant number, since it is smaller than the sum of its proper divisors (260064).

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

102816 is a wasteful number, since it uses less digits than its factorization.

102816 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 43 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 18.

The square root of 102816 is about 320.6493411813. The cubic root of 102816 is about 46.8475519307.

The spelling of 102816 in words is "one hundred two thousand, eight hundred sixteen".