385257600 has 768 divisors, whose sum is σ = 1770720000. Its totient is φ = 81285120.

The previous prime is 385257599. The next prime is 385257629. The reversal of 385257600 is 6752583.

385257600 is a `hidden beast` number, since 3 + 85 + 2 + 576 + 0 + 0 = 666.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 29635194 + ... + 29635206.

It is an arithmetic number, because the mean of its divisors is an integer number (2305625).

Almost surely, 2^385257600 is an apocalyptic number.

385257600 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 385257600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (885360000).

385257600 is an abundant number, since it is smaller than the sum of its proper divisors (1385462400).

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

385257600 is a wasteful number, since it uses less digits than its factorization.

385257600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 67 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 50400, while the sum is 36.

The square root of 385257600 is about 19627.9800285205. The cubic root of 385257600 is about 727.6408484864.

The spelling of 385257600 in words is "three hundred eighty-five million, two hundred fifty-seven thousand, six hundred".