82576800 has 144 divisors (see below), whose sum is σ = 298730880. Its totient is φ = 22014720.

The previous prime is 82576789. The next prime is 82576801. The reversal of 82576800 is 867528.

82576800 is a `hidden beast` number, since 8 + 2 + 576 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (144).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (82576801) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 19689 + ... + 23511.

It is an arithmetic number, because the mean of its divisors is an integer number (2074520).

Almost surely, 2^82576800 is an apocalyptic number.

82576800 is a gapful number since it is divisible by the number (80) 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 82576800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149365440).

82576800 is an abundant number, since it is smaller than the sum of its proper divisors (216154080).

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

82576800 is a wasteful number, since it uses less digits than its factorization.

82576800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3852 (or 3833 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 36.

The square root of 82576800 is about 9087.1777797070. The cubic root of 82576800 is about 435.4644266906.

The spelling of 82576800 in words is "eighty-two million, five hundred seventy-six thousand, eight hundred".