82656 has 72 divisors (see below), whose sum is σ = 275184. Its totient is φ = 23040.

The previous prime is 82651. The next prime is 82657. The reversal of 82656 is 65628.

82656 is a `hidden beast` number, since 8 + 2 + 656 = 666.

It is a tau number, because it is divible by the number of its divisors (72).

Its product of digits (2880) is a multiple of the sum of its prime factors (64).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82651) by changing a digit.

82656 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a Kaprekar number, because its square (6832014336) can be partitioned into two parts whose sum is 82656.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1996 + ... + 2036.

It is an arithmetic number, because the mean of its divisors is an integer number (3822).

2⁸²⁶⁵⁶ is an apocalyptic number.

It is a pronic number, being equal to 287×288.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82656, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137592).

82656 is an abundant number, since it is smaller than the sum of its proper divisors (192528).

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

82656 is a wasteful number, since it uses less digits than its factorization.

82656 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 64 (or 53 counting only the distinct ones).

The product of its digits is 2880, while the sum is 27.

The square root of 82656 is about 287.4995652171. The cubic root of 82656 is about 43.5603601222.

The spelling of 82656 in words is "eighty-two thousand, six hundred fifty-six".