384688800 has 324 divisors, whose sum is σ = 1432091934. Its totient is φ = 97152000.

The previous prime is 384688789. The next prime is 384688807. The reversal of 384688800 is 8886483.

It can be written as a sum of positive squares in 3 ways, for example, as 362673936 + 22014864 = 19044^2 + 4692^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (384688807) by changing a digit.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 3808750 + ... + 3808850.

Almost surely, 2^384688800 is an apocalyptic number.

384688800 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 384688800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (716045967).

384688800 is an abundant number, since it is smaller than the sum of its proper divisors (1047403134).

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

384688800 is a wasteful number, since it uses less digits than its factorization.

384688800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 173 (or 134 counting only the distinct ones).

The product of its (nonzero) digits is 294912, while the sum is 45.

The square root of 384688800 is about 19613.4851569016. The cubic root of 384688800 is about 727.2825722152.

The spelling of 384688800 in words is "three hundred eighty-four million, six hundred eighty-eight thousand, eight hundred".