509968000 has 64 divisors (see below), whose sum is σ = 1267947720. Its totient is φ = 203980800.

The previous prime is 509967979. The next prime is 509968009. The reversal of 509968000 is 869905.

It can be written as a sum of positive squares in 4 ways, for example, as 86266944 + 423701056 = 9288^2 + 20584^2 .

It is a tau number, because it is divible by the number of its divisors (64).

It is a super-2 number, since 2×509968000² = 520134722048000000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (509968009) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 64 + ... + 31936.

Almost surely, 2^509968000 is an apocalyptic number.

509968000 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 509968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (633973860).

509968000 is an abundant number, since it is smaller than the sum of its proper divisors (757979720).

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

509968000 is an equidigital number, since it uses as much as digits as its factorization.

509968000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 31902 (or 31880 counting only the distinct ones).

The product of its (nonzero) digits is 19440, while the sum is 37.

The square root of 509968000 is about 22582.4710782501. The cubic root of 509968000 is about 798.9402634847.

It can be divided in two parts, 50996 and 8000, that added together give a triangular number (58996 = T₃₄₃).

The spelling of 509968000 in words is "five hundred nine million, nine hundred sixty-eight thousand".