385842137702400 has 1008 divisors, whose sum is σ = 1418277262179960. Its totient is φ = 100205907148800.

The previous prime is 385842137702383. The next prime is 385842137702467. The reversal of 385842137702400 is 4207731248583.

It is a happy number.

385842137702400 is a `hidden beast` number, since 3 + 8 + 5 + 8 + 4 + 21 + 377 + 0 + 240 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 126231157149696 + 259610980552704 = 11235264^2 + 16112448^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 46325141436 + ... + 46325149764.

Almost surely, 2^{385842137702400} is an apocalyptic number.

385842137702400 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 385842137702400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (709138631089980).

385842137702400 is an abundant number, since it is smaller than the sum of its proper divisors (1032435124477560).

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

385842137702400 is a wasteful number, since it uses less digits than its factorization.

385842137702400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 9025 (or 8993 counting only the distinct ones).

The product of its (nonzero) digits is 9031680, while the sum is 54.

The spelling of 385842137702400 in words is "three hundred eighty-five trillion, eight hundred forty-two billion, one hundred thirty-seven million, seven hundred two thousand, four hundred".