81864 has 32 divisors (see below), whose sum is σ = 228000. Its totient is φ = 27216.

The previous prime is 81853. The next prime is 81869. The reversal of 81864 is 46818.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits.

Its product of digits (1536) is a multiple of the sum of its prime divisors (384).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 81864.

It is not an unprimeable number, because it can be changed into a prime (81869) by changing a digit.

81864 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 7 ways as a sum of consecutive naturals, for example, 27 + ... + 405.

It is an arithmetic number, because the mean of its divisors is an integer number (7125).

2⁸¹⁸⁶⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 81864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (114000).

81864 is an abundant number, since it is smaller than the sum of its proper divisors (146136).

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

81864 is a wasteful number, since it uses less digits than its factorization.

81864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 394 (or 384 counting only the distinct ones).

The product of its digits is 1536, while the sum is 27.

The square root of 81864 is about 286.1188564216. The cubic root of 81864 is about 43.4207832954.

The spelling of 81864 in words is "eighty-one thousand, eight hundred sixty-four".