82568102400 has 1440 divisors, whose sum is σ = 377572440960. Its totient is φ = 16774594560.

The previous prime is 82568102359. The next prime is 82568102429. The reversal of 82568102400 is 420186528.

82568102400 is a `hidden beast` number, since 82 + 568 + 10 + 2 + 4 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1440).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 260467042 + ... + 260467358.

It is an arithmetic number, because the mean of its divisors is an integer number (262203084).

Almost surely, 2^82568102400 is an apocalyptic number.

82568102400 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 82568102400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (188786220480).

82568102400 is an abundant number, since it is smaller than the sum of its proper divisors (295004338560).

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

82568102400 is a wasteful number, since it uses less digits than its factorization.

82568102400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 394 (or 370 counting only the distinct ones).

The product of its (nonzero) digits is 30720, while the sum is 36.

Adding to 82568102400 its reverse (420186528), we get a palindrome (82988288928).

The spelling of 82568102400 in words is "eighty-two billion, five hundred sixty-eight million, one hundred two thousand, four hundred".