509280 has 48 divisors (see below), whose sum is σ = 1605744. Its totient is φ = 135680.

The previous prime is 509263. The next prime is 509281. The reversal of 509280 is 82905.

It is a tau number, because it is divible by the number of its divisors (48).

It is a super-2 number, since 2×509280² = 518732236800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a self number, because there is not a number n which added to its sum of digits gives 509280.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (509281) 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, 51 + ... + 1010.

It is an arithmetic number, because the mean of its divisors is an integer number (33453).

2⁵⁰⁹²⁸⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 509280, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (802872).

509280 is an abundant number, since it is smaller than the sum of its proper divisors (1096464).

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

509280 is a wasteful number, since it uses less digits than its factorization.

509280 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1079 (or 1071 counting only the distinct ones).

The product of its (nonzero) digits is 720, while the sum is 24.

The square root of 509280 is about 713.6385639804. The cubic root of 509280 is about 79.8580817222.

The spelling of 509280 in words is "five hundred nine thousand, two hundred eighty".