384414816000 has 288 divisors, whose sum is σ = 1278374243328. Its totient is φ = 102386995200.

The previous prime is 384414815971. The next prime is 384414816007. The reversal of 384414816000 is 618414483.

It is a self number, because there is not a number n which added to its sum of digits gives 384414816000.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (384414816007) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 102046117 + ... + 102049883.

It is an arithmetic number, because the mean of its divisors is an integer number (4438799456).

Almost surely, 2^384414816000 is an apocalyptic number.

384414816000 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 384414816000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (639187121664).

384414816000 is an abundant number, since it is smaller than the sum of its proper divisors (893959427328).

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

384414816000 is a wasteful number, since it uses less digits than its factorization.

384414816000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4864 (or 4840 counting only the distinct ones).

The product of its (nonzero) digits is 73728, while the sum is 39.

The spelling of 384414816000 in words is "three hundred eighty-four billion, four hundred fourteen million, eight hundred sixteen thousand".