509688 has 24 divisors (see below), whose sum is σ = 1380600. Its totient is φ = 169872.

The previous prime is 509687. The next prime is 509689. The reversal of 509688 is 886905.

509688 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (509687) and next prime (509689).

It is a tau number, because it is divible by the number of its divisors (24).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 509688.

It is not an unprimeable number, because it can be changed into a prime (509681) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 3468 + ... + 3611.

It is an arithmetic number, because the mean of its divisors is an integer number (57525).

2⁵⁰⁹⁶⁸⁸ is an apocalyptic number.

It is an amenable number.

509688 is an abundant number, since it is smaller than the sum of its proper divisors (870912).

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

509688 is a wasteful number, since it uses less digits than its factorization.

509688 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 7091 (or 7084 counting only the distinct ones).

The product of its (nonzero) digits is 17280, while the sum is 36.

The square root of 509688 is about 713.9243657419. The cubic root of 509688 is about 79.8794016251.

It can be divided in two parts, 5096 and 88, that added together give a square (5184 = 72²).

The spelling of 509688 in words is "five hundred nine thousand, six hundred eighty-eight".