8205818400 has 864 divisors, whose sum is σ = 34395798528. Its totient is φ = 1891123200.

The previous prime is 8205818381. The next prime is 8205818459. The reversal of 8205818400 is 48185028.

It is a tau number, because it is divible by the number of its divisors (864).

It is a super-2 number, since 2×8205818400² (a number of 21 digits) contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 42962305 + ... + 42962495.

It is an arithmetic number, because the mean of its divisors is an integer number (39809952).

Almost surely, 2^8205818400 is an apocalyptic number.

8205818400 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 8205818400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17197899264).

8205818400 is an abundant number, since it is smaller than the sum of its proper divisors (26189980128).

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

8205818400 is a wasteful number, since it uses less digits than its factorization.

8205818400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 256 (or 231 counting only the distinct ones).

The product of its (nonzero) digits is 20480, while the sum is 36.

The square root of 8205818400 is about 90585.9724239907. The cubic root of 8205818400 is about 2017.0065127087.

The spelling of 8205818400 in words is "eight billion, two hundred five million, eight hundred eighteen thousand, four hundred".