393984000 has 480 divisors, whose sum is σ = 1545944400. Its totient is φ = 99532800.

The previous prime is 393983999. The next prime is 393984013. The reversal of 393984000 is 489393.

It is a tau number, because it is divible by the number of its divisors (480).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 20735991 + ... + 20736009.

Almost surely, 2^393984000 is an apocalyptic number.

393984000 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 393984000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (772972200).

393984000 is an abundant number, since it is smaller than the sum of its proper divisors (1151960400).

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

393984000 is an equidigital number, since it uses as much as digits as its factorization.

393984000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 68 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 23328, while the sum is 36.

The square root of 393984000 is about 19849.0302030099. The cubic root of 393984000 is about 733.0937693148.

The spelling of 393984000 in words is "three hundred ninety-three million, nine hundred eighty-four thousand".