83856384000 has 672 divisors, whose sum is σ = 314438787936. Its totient is φ = 22295347200.

The previous prime is 83856383987. The next prime is 83856384011. The reversal of 83856384000 is 48365838.

83856384000 is a `hidden beast` number, since 8 + 3 + 8 + 5 + 638 + 4 + 0 + 0 + 0 = 666.

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

It is a congruent number.

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 47 ways as a sum of consecutive naturals, for example, 248831832 + ... + 248832168.

It is an arithmetic number, because the mean of its divisors is an integer number (467914863).

Almost surely, 2^83856384000 is an apocalyptic number.

83856384000 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 83856384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (157219393968).

83856384000 is an abundant number, since it is smaller than the sum of its proper divisors (230582403936).

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

83856384000 is an frugal number, since it uses more digits than its factorization.

83856384000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 393 (or 347 counting only the distinct ones).

The product of its (nonzero) digits is 552960, while the sum is 45.

It can be divided in two parts, 83856 and 384000, that added together give a square (467856 = 684²).

The spelling of 83856384000 in words is "eighty-three billion, eight hundred fifty-six million, three hundred eighty-four thousand".