509408870400 has 672 divisors, whose sum is σ = 1896326133870. Its totient is φ = 135683112960.

The previous prime is 509408870389. The next prime is 509408870419. The reversal of 509408870400 is 4078804905.

It can be written as a sum of positive squares in 3 ways, for example, as 244241547264 + 265167323136 = 494208^2 + 514944^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

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 41 ways as a sum of consecutive naturals, for example, 597196374 + ... + 597197226.

Almost surely, 2^509408870400 is an apocalyptic number.

509408870400 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 509408870400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (948163066935).

509408870400 is an abundant number, since it is smaller than the sum of its proper divisors (1386917263470).

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

509408870400 is an frugal number, since it uses more digits than its factorization.

509408870400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 911 (or 863 counting only the distinct ones).

The product of its (nonzero) digits is 322560, while the sum is 45.

The spelling of 509408870400 in words is "five hundred nine billion, four hundred eight million, eight hundred seventy thousand, four hundred".