509447078400 has 960 divisors, whose sum is σ = 1935647860608. Its totient is φ = 117005352960.

The previous prime is 509447078369. The next prime is 509447078411. The reversal of 509447078400 is 4870744905.

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 (48).

It is a self number, because there is not a number n which added to its sum of digits gives 509447078400.

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, 1468147027 + ... + 1468147373.

Almost surely, 2^509447078400 is an apocalyptic number.

509447078400 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 509447078400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (967823930304).

509447078400 is an abundant number, since it is smaller than the sum of its proper divisors (1426200782208).

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

509447078400 is a wasteful number, since it uses less digits than its factorization.

509447078400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 581 (or 560 counting only the distinct ones).

The product of its (nonzero) digits is 1128960, while the sum is 48.

The spelling of 509447078400 in words is "five hundred nine billion, four hundred forty-seven million, seventy-eight thousand, four hundred".