82944 has 55 divisors (see below), whose sum is σ = 247687. Its totient is φ = 27648.

The previous prime is 82939. The next prime is 82963. The reversal of 82944 is 44928.

82944 = T_{287} + T_{288}.

The square root of 82944 is 288.

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!)^{3} ⋅ 3!.

82944 is an esthetic number in base 5, because in such base its adjacent digits differ by 1.

It is an ABA number since it can be written as A⋅B^{A}, here for A=4, B=12.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a Duffinian number.

Its product of digits (2304) is a multiple of the sum of its prime factors (32).

It is a nialpdrome in base 12.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 82944.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 4 ways as a sum of consecutive naturals, for example, 27647 + 27648 + 27649.

82944 is a Friedman number, since it can be written as (9*8)^2*4*4, using all its digits and the basic arithmetic operations.

2^{82944} is an apocalyptic number.

82944 is the 288-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82944

82944 is an abundant number, since it is smaller than the sum of its proper divisors (164743).

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

82944 is an equidigital number, since it uses as much as digits as its factorization.

82944 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 32 (or 5 counting only the distinct ones).

The product of its digits is 2304, while the sum is 27.

The cubic root of 82944 is about 43.6108942280.

Multiplying 82944 by its product of digits (2304), we get a 6-th power (191102976 = 24^{6}).

82944 divided by its product of digits (2304) gives a triangular number (36 = T_{8}).

The spelling of 82944 in words is "eighty-two thousand, nine hundred forty-four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192 216 256 288 324 384 432 512 576 648 768 864 1024 1152 1296 1536 1728 2304 2592 3072 3456 4608 5184 6912 9216 10368 13824 20736 27648 41472 82944

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