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32768 = 215

32768 has 16 divisors (see below), whose sum is σ = 65535. Its totient is φ = 16384.

The previous prime is 32749. The next prime is 32771. The reversal of 32768 is 86723.

The cubic root of 32768 is 32.

It is a perfect power (a cube, a 5-th power, a 15-th power), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as (2!)15.

32768 is an esthetic number in base 15, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 16384 + 16384 = 128^2 + 128^2 .

It is a tau number, because it is divible by the number of its divisors (16).

It is an ABA number since it can be written as A⋅BA, here for A=2, B=128.

It is a Duffinian number.

Its product of digits (2016) is a multiple of the sum of its prime divisors (2).

It is a plaindrome in base 11.

It is a nialpdrome in base 2, base 4, base 8 and base 16.

It is a zygodrome in base 3.

It is an unprimeable number.

In principle, a polygon with 32768 sides can be constructed with ruler and compass.

It is an impolite number, since it cannot be written as a nontrivial sum of consecutive naturals.

32768 is a Friedman number, since it can be written as (2^(8-7-6))^(-3), using all its digits and the basic arithmetic operations.

232768 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 32768

32768 is a deficient number, since it is larger than the sum of its proper divisors (32767).

32768 is an frugal number, since it uses more digits than its factorization.

32768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 30 (or 2 counting only the distinct ones).

The product of its digits is 2016, while the sum is 26.

The square root of 32768 is about 181.0193359838.

The spelling of 32768 in words is "thirty-two thousand, seven hundred sixty-eight".

Divisors: 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768