509350461043200 has 960 divisors, whose sum is σ = 1929057856585728. Its totient is φ = 116055642931200.

The previous prime is 509350461043103. The next prime is 509350461043219. The reversal of 509350461043200 is 2340164053905.

It is a tau number, because it is divible by the number of its divisors (960).

It is a Harshad number since it is a multiple of its sum of digits (42).

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 128396887617 + ... + 128396891583.

Almost surely, 2^{509350461043200} is an apocalyptic number.

509350461043200 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 509350461043200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (964528928292864).

509350461043200 is an abundant number, since it is smaller than the sum of its proper divisors (1419707395542528).

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

509350461043200 is a wasteful number, since it uses less digits than its factorization.

509350461043200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5393 (or 5372 counting only the distinct ones).

The product of its (nonzero) digits is 388800, while the sum is 42.

The spelling of 509350461043200 in words is "five hundred nine trillion, three hundred fifty billion, four hundred sixty-one million, forty-three thousand, two hundred".