36864 has 39 divisors (see below), whose sum is σ = 106483. Its totient is φ = 12288.

The previous prime is 36857. The next prime is 36871. The reversal of 36864 is 46863.

36864 = T_{191} + T_{192}.

The square root of 36864 is 192.

It is a perfect power (a square), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as (4!)^{2} ⋅ (2!)^{6}.

It is an interprime number because it is at equal distance from previous prime (36857) and next prime (36871).

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

It is a Duffinian number.

It is a nialpdrome in base 4, base 8, base 9 and base 16.

It is a zygodrome in base 8.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 36864.

It is an unprimeable number.

36864 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 12287 + 12288 + 12289.

36864 is a Friedman number, since it can be written as (8*6*4)^(6/3), using all its digits and the basic arithmetic operations.

2^{36864} is an apocalyptic number.

36864 is the 192-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 36864

36864 is an abundant number, since it is smaller than the sum of its proper divisors (69619).

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

36864 is an equidigital number, since it uses as much as digits as its factorization.

36864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30 (or 5 counting only the distinct ones).

The product of its digits is 3456, while the sum is 27.

The cubic root of 36864 is about 33.2813411688.

Subtracting 36864 from its reverse (46863), we obtain a palindrome (9999).

It can be divided in two parts, 36 and 864, that added together give a square (900 = 30^{2}).

The spelling of 36864 in words is "thirty-six thousand, eight hundred sixty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 128 144 192 256 288 384 512 576 768 1024 1152 1536 2048 2304 3072 4096 4608 6144 9216 12288 18432 36864

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