82585600 has 72 divisors (see below), whose sum is σ = 204889230. Its totient is φ = 33013760.

The previous prime is 82585589. The next prime is 82585621. The reversal of 82585600 is 658528.

It can be written as a sum of positive squares in 3 ways, for example, as 65545216 + 17040384 = 8096^2 + 4128^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 50394 + ... + 52006.

Almost surely, 2^82585600 is an apocalyptic number.

82585600 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 82585600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (102444615).

82585600 is an abundant number, since it is smaller than the sum of its proper divisors (122303630).

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

82585600 is a wasteful number, since it uses less digits than its factorization.

82585600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1645 (or 1620 counting only the distinct ones).

The product of its (nonzero) digits is 19200, while the sum is 34.

The square root of 82585600 is about 9087.6619655443. The cubic root of 82585600 is about 435.4798949207.

The spelling of 82585600 in words is "eighty-two million, five hundred eighty-five thousand, six hundred".