27264 has 32 divisors (see below), whose sum is σ = 73440. Its totient is φ = 8960.

The previous prime is 27259. The next prime is 27271. The reversal of 27264 is 46272.

Adding to 27264 its reverse (46272), we get a triangular number (73536 = T_{383}).

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (32).

It is a nialpdrome in base 8 and base 13.

It is a self number, because there is not a number *n* which added to its sum of digits gives 27264.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 349 + ... + 419.

It is an arithmetic number, because the mean of its divisors is an integer number (2295).

2^{27264} is an apocalyptic number.

27264 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 27264, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (36720).

27264 is an abundant number, since it is smaller than the sum of its proper divisors (46176).

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

27264 is an equidigital number, since it uses as much as digits as its factorization.

27264 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 88 (or 76 counting only the distinct ones).

The product of its digits is 672, while the sum is 21.

The square root of 27264 is about 165.1181395244. The cubic root of 27264 is about 30.0974608146.

The spelling of 27264 in words is "twenty-seven thousand, two hundred sixty-four".

Divisors: 1 2 3 4 6 8 12 16 24 32 48 64 71 96 128 142 192 213 284 384 426 568 852 1136 1704 2272 3408 4544 6816 9088 13632 27264

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