384816000 has 128 divisors (see below), whose sum is σ = 1275824160. Its totient is φ = 102604800.

The previous prime is 384815983. The next prime is 384816007. The reversal of 384816000 is 618483.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (128).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (384816007) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 43992 + ... + 52008.

Almost surely, 2^384816000 is an apocalyptic number.

384816000 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 384816000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (637912080).

384816000 is an abundant number, since it is smaller than the sum of its proper divisors (891008160).

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

384816000 is an equidigital number, since it uses as much as digits as its factorization.

384816000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 8049 (or 8027 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 30.

The square root of 384816000 is about 19616.7275558387. The cubic root of 384816000 is about 727.3627237114.

The spelling of 384816000 in words is "three hundred eighty-four million, eight hundred sixteen thousand".