509528678400 has 2016 divisors, whose sum is σ = 2327407250688. Its totient is φ = 103809024000.

The previous prime is 509528678371. The next prime is 509528678401. The reversal of 509528678400 is 4876825905.

509528678400 is a `hidden beast` number, since 5 + 0 + 9 + 528 + 6 + 78 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2016).

It is a super-2 number, since 2×509528678400² (a number of 24 digits) contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (509528678401) by changing a digit.

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 143 ways as a sum of consecutive naturals, for example, 5044838350 + ... + 5044838450.

Almost surely, 2^509528678400 is an apocalyptic number.

509528678400 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 509528678400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1163703625344).

509528678400 is an abundant number, since it is smaller than the sum of its proper divisors (1817878572288).

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

509528678400 is a wasteful number, since it uses less digits than its factorization.

509528678400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 190 (or 158 counting only the distinct ones).

The product of its (nonzero) digits is 4838400, while the sum is 54.

The spelling of 509528678400 in words is "five hundred nine billion, five hundred twenty-eight million, six hundred seventy-eight thousand, four hundred".