384681600 has 432 divisors, whose sum is σ = 1487831670. Its totient is φ = 94556160.

The previous prime is 384681571. The next prime is 384681611. The reversal of 384681600 is 6186483.

It is a happy number.

384681600 is a `hidden beast` number, since 3 + 8 + 46 + 8 + 1 + 600 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 349540416 + 35141184 = 18696^2 + 5928^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 10396782 + ... + 10396818.

Almost surely, 2^384681600 is an apocalyptic number.

384681600 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 384681600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (743915835).

384681600 is an abundant number, since it is smaller than the sum of its proper divisors (1103150070).

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

384681600 is a wasteful number, since it uses less digits than its factorization.

384681600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 105 (or 66 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 384681600 is about 19613.3016088572. The cubic root of 384681600 is about 727.2780348098.

The spelling of 384681600 in words is "three hundred eighty-four million, six hundred eighty-one thousand, six hundred".