393984 has 90 divisors (see below), whose sum is σ = 1236620. Its totient is φ = 124416.

The previous prime is 393977. The next prime is 393989. The reversal of 393984 is 489393.

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

It is a nude number because it is divisible by every one of its digits.

Its product of digits (23328) is a multiple of the sum of its prime divisors (24).

It is a zygodrome in base 2.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 393984.

It is not an unprimeable number, because it can be changed into a prime (393989) by changing a digit.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 20727 + ... + 20745.

393984 is a Friedman number, since it can be written as (9*3-8)*(9+3)^4, using all its digits and the basic arithmetic operations.

2³⁹³⁹⁸⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 393984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (618310).

393984 is an abundant number, since it is smaller than the sum of its proper divisors (842636).

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

393984 is an equidigital number, since it uses as much as digits as its factorization.

393984 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 47 (or 24 counting only the distinct ones).

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

The square root of 393984 is about 627.6814478699. The cubic root of 393984 is about 73.3093769315.

The spelling of 393984 in words is "three hundred ninety-three thousand, nine hundred eighty-four".