509760 has 112 divisors (see below), whose sum is σ = 1828800. Its totient is φ = 133632.

The previous prime is 509741. The next prime is 509767. The reversal of 509760 is 67905.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (509767) by changing a digit.

509760 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 8611 + ... + 8669.

2⁵⁰⁹⁷⁶⁰ 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 509760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (914400).

509760 is an abundant number, since it is smaller than the sum of its proper divisors (1319040).

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

509760 is a wasteful number, since it uses less digits than its factorization.

509760 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 85 (or 69 counting only the distinct ones).

The product of its (nonzero) digits is 1890, while the sum is 27.

The square root of 509760 is about 713.9747894709. The cubic root of 509760 is about 79.8831627797.

The spelling of 509760 in words is "five hundred nine thousand, seven hundred sixty".