84384000 has 216 divisors, whose sum is σ = 304674552. Its totient is φ = 22425600.

The previous prime is 84383989. The next prime is 84384023. The reversal of 84384000 is 48348.

It can be written as a sum of positive squares in 4 ways, for example, as 331776 + 84052224 = 576^2 + 9168^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 287854 + ... + 288146.

Almost surely, 2^84384000 is an apocalyptic number.

84384000 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 84384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (152337276).

84384000 is an abundant number, since it is smaller than the sum of its proper divisors (220290552).

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

84384000 is a wasteful number, since it uses less digits than its factorization.

84384000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 330 (or 303 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 84384000 is about 9186.0764203222. The cubic root of 84384000 is about 438.6182549388.

The spelling of 84384000 in words is "eighty-four million, three hundred eighty-four thousand".