509520000 has 320 divisors, whose sum is σ = 1854531360. Its totient is φ = 122880000.

The previous prime is 509519993. The next prime is 509520001. The reversal of 509520000 is 25905.

It is a tau number, because it is divible by the number of its divisors (320).

It is a super-2 number, since 2×509520000² = 519221260800000000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (509520001) 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 39 ways as a sum of consecutive naturals, for example, 2639904 + ... + 2640096.

Almost surely, 2^509520000 is an apocalyptic number.

509520000 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 509520000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (927265680).

509520000 is an abundant number, since it is smaller than the sum of its proper divisors (1345011360).

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

509520000 is a wasteful number, since it uses less digits than its factorization.

509520000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 241 (or 214 counting only the distinct ones).

The product of its (nonzero) digits is 450, while the sum is 21.

The square root of 509520000 is about 22572.5497009088. The cubic root of 509520000 is about 798.7062421996.

Adding to 509520000 its reverse (25905), we get a palindrome (509545905).

The spelling of 509520000 in words is "five hundred nine million, five hundred twenty thousand".