204864 has 56 divisors (see below), whose sum is σ = 597408. Its totient is φ = 61440.

The previous prime is 204859. The next prime is 204871. The reversal of 204864 is 468402.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2064 + ... + 2160.

It is an arithmetic number, because the mean of its divisors is an integer number (10668).

204864 is a Friedman number, since it can be written as 6402*8*4, using all its digits and the basic arithmetic operations.

2²⁰⁴⁸⁶⁴ is an apocalyptic number.

204864 is a gapful number since it is divisible by the number (24) 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 204864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (298704).

204864 is an abundant number, since it is smaller than the sum of its proper divisors (392544).

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

204864 is a wasteful number, since it uses less digits than its factorization.

204864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 123 (or 113 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 24.

The square root of 204864 is about 452.6190451141. The cubic root of 204864 is about 58.9506433913.

It can be divided in two parts, 2048 and 64, that multiplied together give a 17-th power (131072 = 2¹⁷).

The spelling of 204864 in words is "two hundred four thousand, eight hundred sixty-four".