509359104000 has 1344 divisors, whose sum is σ = 2009431307520. Its totient is φ = 128463667200.

The previous prime is 509359103923. The next prime is 509359104013. The reversal of 509359104000 is 401953905.

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 5723135956 + ... + 5723136044.

It is an arithmetic number, because the mean of its divisors is an integer number (1495112580).

Almost surely, 2^509359104000 is an apocalyptic number.

509359104000 is a gapful number since it is divisible by the number (50) 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 509359104000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1004715653760).

509359104000 is an abundant number, since it is smaller than the sum of its proper divisors (1500072203520).

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

509359104000 is an frugal number, since it uses more digits than its factorization.

509359104000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 168 (or 122 counting only the distinct ones).

The product of its (nonzero) digits is 24300, while the sum is 36.

The spelling of 509359104000 in words is "five hundred nine billion, three hundred fifty-nine million, one hundred four thousand".