188064 has 36 divisors (see below), whose sum is σ = 535626. Its totient is φ = 62592.

The previous prime is 188029. The next prime is 188107. The reversal of 188064 is 460881.

188064 is digitally balanced in base 2 and base 3, because in such bases it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 176400 + 11664 = 420^2 + 108^2 .

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

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 188064.

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 39 + ... + 614.

2¹⁸⁸⁰⁶⁴ 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 188064, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (267813).

188064 is an abundant number, since it is smaller than the sum of its proper divisors (347562).

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

188064 is a wasteful number, since it uses less digits than its factorization.

188064 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 669 (or 658 counting only the distinct ones).

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

The square root of 188064 is about 433.6634639902. The cubic root of 188064 is about 57.2930430229.

The spelling of 188064 in words is "one hundred eighty-eight thousand, sixty-four".