86187628800 has 2268 divisors, whose sum is σ = 414502259220. Its totient is φ = 17557585920.

The previous prime is 86187628799. The next prime is 86187628831. The reversal of 86187628800 is 882678168.

86187628800 is a `hidden beast` number, since 8 + 6 + 1 + 8 + 7 + 628 + 8 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 8787937536 + 77399691264 = 93744^2 + 278208^2 .

It is a tau number, because it is divible by the number of its divisors (2268).

It is a Harshad number since it is a multiple of its sum of digits (54).

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 251 ways as a sum of consecutive naturals, for example, 2971987186 + ... + 2971987214.

Almost surely, 2^86187628800 is an apocalyptic number.

86187628800 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 86187628800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (207251129610).

86187628800 is an abundant number, since it is smaller than the sum of its proper divisors (328314630420).

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

86187628800 is a wasteful number, since it uses less digits than its factorization.

86187628800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 100 (or 59 counting only the distinct ones).

The product of its (nonzero) digits is 2064384, while the sum is 54.

The spelling of 86187628800 in words is "eighty-six billion, one hundred eighty-seven million, six hundred twenty-eight thousand, eight hundred".