384000 has 88 divisors (see below), whose sum is σ = 1277328. Its totient is φ = 102400.

The previous prime is 383987. The next prime is 384001. The reversal of 384000 is 483.

384000 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (384001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 76798 + ... + 76802.

2³⁸⁴⁰⁰⁰ is an apocalyptic number.

384000 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 384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (638664).

384000 is an abundant number, since it is smaller than the sum of its proper divisors (893328).

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

384000 is an equidigital number, since it uses as much as digits as its factorization.

384000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 38 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 384000 is about 619.6773353932. The cubic root of 384000 is about 72.6848237133.

Multiplying 384000 by its sum of digits (15), we get a square (5760000 = 2400²).

384000 divided by its sum of digits (15) gives a square (25600 = 160²).

Adding to 384000 its reverse (483), we get a palindrome (384483).

The spelling of 384000 in words is "three hundred eighty-four thousand".