82185062400 has 1440 divisors, whose sum is σ = 368648280000. Its totient is φ = 17677025280.

The previous prime is 82185062371. The next prime is 82185062413. The reversal of 82185062400 is 426058128.

82185062400 is a `hidden beast` number, since 8 + 21 + 8 + 5 + 0 + 624 + 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 (11) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 551577526 + ... + 551577674.

It is an arithmetic number, because the mean of its divisors is an integer number (256005750).

Almost surely, 2^82185062400 is an apocalyptic number.

82185062400 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 82185062400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (184324140000).

82185062400 is an abundant number, since it is smaller than the sum of its proper divisors (286463217600).

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

82185062400 is a wasteful number, since it uses less digits than its factorization.

82185062400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 219 (or 185 counting only the distinct ones).

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

The spelling of 82185062400 in words is "eighty-two billion, one hundred eighty-five million, sixty-two thousand, four hundred".