385905600 has 168 divisors, whose sum is σ = 1406926320. Its totient is φ = 102896640.

The previous prime is 385905589. The next prime is 385905617. The reversal of 385905600 is 6509583.

385905600 is a `hidden beast` number, since 3 + 8 + 5 + 90 + 560 + 0 = 666.

It is a super-2 number, since 2×385905600² = 297846264222720000, which contains 22 as substring.

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

It is a zygodrome in base 3.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 38734 + ... + 47666.

Almost surely, 2^385905600 is an apocalyptic number.

385905600 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 385905600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (703463160).

385905600 is an abundant number, since it is smaller than the sum of its proper divisors (1021020720).

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

385905600 is a wasteful number, since it uses less digits than its factorization.

385905600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 8964 (or 8943 counting only the distinct ones).

The product of its (nonzero) digits is 32400, while the sum is 36.

The square root of 385905600 is about 19644.4801407418. The cubic root of 385905600 is about 728.0485818724.

The spelling of 385905600 in words is "three hundred eighty-five million, nine hundred five thousand, six hundred".