12864 has 28 divisors (see below), whose sum is σ = 34544. Its totient is φ = 4224.

The previous prime is 12853. The next prime is 12889. The reversal of 12864 is 46821.

Added to its reverse (46821) it gives a triangular number (59685 = T_{345}).

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

It is one of the 548 Lynch-Bell numbers.

It is a nialpdrome in base 8 and base 12.

It is a self number, because there is not a number *n* which added to its sum of digits gives 12864.

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 159 + ... + 225.

2^{12864} 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 12864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17272).

12864 is an abundant number, since it is smaller than the sum of its proper divisors (21680).

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

12864 is an equidigital number, since it uses as much as digits as its factorization.

12864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 82 (or 72 counting only the distinct ones).

The product of its digits is 384, while the sum is 21.

The square root of 12864 is about 113.4195750301. The cubic root of 12864 is about 23.4310640106.

Adding to 12864 its reverse (46821), we get a triangular number (59685 = T_{345}).

It can be divided in two parts, 128 and 64, that multiplied together give a 13-th power (8192 = 2^{13}).

The spelling of 12864 in words is "twelve thousand, eight hundred sixty-four".

Divisors: 1 2 3 4 6 8 12 16 24 32 48 64 67 96 134 192 201 268 402 536 804 1072 1608 2144 3216 4288 6432 12864

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