509027328000 has 1680 divisors, whose sum is σ = 2120805693864. Its totient is φ = 121031884800.

The previous prime is 509027327999. The next prime is 509027328001. The reversal of 509027328000 is 823720905.

It is a happy number.

509027328000 is a `hidden beast` number, since 509 + 0 + 2 + 73 + 2 + 80 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (509027327999) and next prime (509027328001).

It can be written as a sum of positive squares in 4 ways, for example, as 221456830464 + 287570497536 = 470592^2 + 536256^2 .

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

It is not an unprimeable number, because it can be changed into a prime (509027328001) by changing a digit.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 26790911991 + ... + 26790912009.

Almost surely, 2^509027328000 is an apocalyptic number.

509027328000 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 509027328000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1060402846932).

509027328000 is an abundant number, since it is smaller than the sum of its proper divisors (1611778365864).

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

509027328000 is an equidigital number, since it uses as much as digits as its factorization.

509027328000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 108 (or 46 counting only the distinct ones).

The product of its (nonzero) digits is 30240, while the sum is 36.

The spelling of 509027328000 in words is "five hundred nine billion, twenty-seven million, three hundred twenty-eight thousand".