385545600 has 288 divisors, whose sum is σ = 1502013240. Its totient is φ = 93388800.

The previous prime is 385545599. The next prime is 385545607. The reversal of 385545600 is 6545583.

385545600 is a `hidden beast` number, since 3 + 8 + 5 + 5 + 45 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (385545607) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 316192 + ... + 317408.

Almost surely, 2^385545600 is an apocalyptic number.

385545600 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 385545600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (751006620).

385545600 is an abundant number, since it is smaller than the sum of its proper divisors (1116467640).

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

385545600 is a wasteful number, since it uses less digits than its factorization.

385545600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1258 (or 1238 counting only the distinct ones).

The product of its (nonzero) digits is 72000, while the sum is 36.

The square root of 385545600 is about 19635.3151235217. The cubic root of 385545600 is about 727.8221197249.

It can be divided in two parts, 3855 and 45600, that added together give a triangular number (49455 = T₃₁₄).

The spelling of 385545600 in words is "three hundred eighty-five million, five hundred forty-five thousand, six hundred".