509952000 has 240 divisors, whose sum is σ = 1717515072. Its totient is φ = 134348800.

The previous prime is 509951999. The next prime is 509952029. The reversal of 509952000 is 259905.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 6143959 + ... + 6144041.

Almost surely, 2^509952000 is an apocalyptic number.

509952000 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 509952000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (858757536).

509952000 is an abundant number, since it is smaller than the sum of its proper divisors (1207563072).

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

509952000 is an frugal number, since it uses more digits than its factorization.

509952000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 129 (or 93 counting only the distinct ones).

The product of its (nonzero) digits is 4050, while the sum is 30.

The square root of 509952000 is about 22582.1168184030. The cubic root of 509952000 is about 798.9319079422.

The spelling of 509952000 in words is "five hundred nine million, nine hundred fifty-two thousand".