384172800 has 432 divisors, whose sum is σ = 1478155392. Its totient is φ = 86835200.

The previous prime is 384172771. The next prime is 384172807. The reversal of 384172800 is 8271483.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is not an unprimeable number, because it can be changed into a prime (384172807) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3590347 + ... + 3590453.

It is an arithmetic number, because the mean of its divisors is an integer number (3421656).

Almost surely, 2^384172800 is an apocalyptic number.

384172800 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 384172800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (739077696).

384172800 is an abundant number, since it is smaller than the sum of its proper divisors (1093982592).

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

384172800 is a wasteful number, since it uses less digits than its factorization.

384172800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 164 (or 145 counting only the distinct ones).

The product of its (nonzero) digits is 10752, while the sum is 33.

The square root of 384172800 is about 19600.3265278923. The cubic root of 384172800 is about 726.9572480184.

The spelling of 384172800 in words is "three hundred eighty-four million, one hundred seventy-two thousand, eight hundred".