82857600 has 384 divisors, whose sum is σ = 349084800. Its totient is φ = 18800640.

The previous prime is 82857539. The next prime is 82857601. The reversal of 82857600 is 675828.

82857600 is a `hidden beast` number, since 82 + 8 + 576 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

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 (82857601) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 604732 + ... + 604868.

It is an arithmetic number, because the mean of its divisors is an integer number (909075).

Almost surely, 2^82857600 is an apocalyptic number.

82857600 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 82857600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (174542400).

82857600 is an abundant number, since it is smaller than the sum of its proper divisors (266227200).

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

82857600 is a wasteful number, since it uses less digits than its factorization.

82857600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 177 (or 154 counting only the distinct ones).

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

The square root of 82857600 is about 9102.6150088862. The cubic root of 82857600 is about 435.9574629545.

The spelling of 82857600 in words is "eighty-two million, eight hundred fifty-seven thousand, six hundred".