3864088800 has 864 divisors, whose sum is σ = 16720179840. Its totient is φ = 858470400.

The previous prime is 3864088771. The next prime is 3864088801. The reversal of 3864088800 is 88804683.

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

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (3864088801) by changing a digit.

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, 27799131 + ... + 27799269.

It is an arithmetic number, because the mean of its divisors is an integer number (19352060).

Almost surely, 2^3864088800 is an apocalyptic number.

3864088800 is a gapful number since it is divisible by the number (30) 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 3864088800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8360089920).

3864088800 is an abundant number, since it is smaller than the sum of its proper divisors (12856091040).

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

3864088800 is a wasteful number, since it uses less digits than its factorization.

3864088800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 198 (or 173 counting only the distinct ones).

The product of its (nonzero) digits is 294912, while the sum is 45.

The square root of 3864088800 is about 62161.7953408683. The cubic root of 3864088800 is about 1569.2146937400.

The spelling of 3864088800 in words is "three billion, eight hundred sixty-four million, eighty-eight thousand, eight hundred".