509345220384 has 1920 divisors, whose sum is σ = 2177186376960. Its totient is φ = 113799168000.

The previous prime is 509345220379. The next prime is 509345220413. The reversal of 509345220384 is 483022543905.

509345220384 is a `hidden beast` number, since 5 + 0 + 9 + 3 + 45 + 220 + 384 = 666.

It is an unprimeable number.

It is a polite number, since it can be written in 319 ways as a sum of consecutive naturals, for example, 5043021934 + ... + 5043022034.

It is an arithmetic number, because the mean of its divisors is an integer number (1133951238).

Almost surely, 2^509345220384 is an apocalyptic number.

509345220384 is a gapful number since it is divisible by the number (54) 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 509345220384, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1088593188480).

509345220384 is an abundant number, since it is smaller than the sum of its proper divisors (1667841156576).

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

509345220384 is a wasteful number, since it uses less digits than its factorization.

509345220384 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 189 (or 154 counting only the distinct ones).

The product of its (nonzero) digits is 1036800, while the sum is 45.

The spelling of 509345220384 in words is "five hundred nine billion, three hundred forty-five million, two hundred twenty thousand, three hundred eighty-four".