10188086400 has 288 divisors, whose sum is σ = 38493713700. Its totient is φ = 2556887040.

The previous prime is 10188086399. The next prime is 10188086413. The reversal of 10188086400 is 468088101.

10188086400 is a `hidden beast` number, since 1 + 0 + 1 + 8 + 8 + 0 + 8 + 640 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 3843008064 + 6345078336 = 61992^2 + 79656^2 .

It is a tau number, because it is divible by the number of its divisors (288).

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

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 479196 + ... + 500004.

Almost surely, 2^10188086400 is an apocalyptic number.

10188086400 is a gapful number since it is divisible by the number (10) 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 10188086400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (19246856850).

10188086400 is an abundant number, since it is smaller than the sum of its proper divisors (28305627300).

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

10188086400 is a wasteful number, since it uses less digits than its factorization.

10188086400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 20856 (or 20836 counting only the distinct ones).

The product of its (nonzero) digits is 12288, while the sum is 36.

The spelling of 10188086400 in words is "ten billion, one hundred eighty-eight million, eighty-six thousand, four hundred".