385005600 has 216 divisors, whose sum is σ = 1551775680. Its totient is φ = 87989760.

The previous prime is 385005559. The next prime is 385005611. The reversal of 385005600 is 6500583.

385005600 is a `hidden beast` number, since 3 + 8 + 50 + 0 + 5 + 600 = 666.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 46581 + ... + 54219.

Almost surely, 2^385005600 is an apocalyptic number.

385005600 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 385005600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (775887840).

385005600 is an abundant number, since it is smaller than the sum of its proper divisors (1166770080).

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

385005600 is a wasteful number, since it uses less digits than its factorization.

385005600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7672 (or 7656 counting only the distinct ones).

The product of its (nonzero) digits is 3600, while the sum is 27.

The square root of 385005600 is about 19621.5595710433. The cubic root of 385005600 is about 727.4821620312.

It can be divided in two parts, 38500 and 5600, that added together give a square (44100 = 210²).

The spelling of 385005600 in words is "three hundred eighty-five million, five thousand, six hundred".