509712 has 80 divisors (see below), whose sum is σ = 1583232. Its totient is φ = 138240.

The previous prime is 509699. The next prime is 509723. The reversal of 509712 is 217905.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 12412 + ... + 12452.

2⁵⁰⁹⁷¹² 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 509712, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (791616).

509712 is an abundant number, since it is smaller than the sum of its proper divisors (1073520).

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

509712 is a wasteful number, since it uses less digits than its factorization.

509712 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 96 (or 90 counting only the distinct ones).

The product of its (nonzero) digits is 630, while the sum is 24.

The square root of 509712 is about 713.9411740473. The cubic root of 509712 is about 79.8806553826.

It can be divided in two parts, 509 and 712, that added together give a palindrome (1221).

The spelling of 509712 in words is "five hundred nine thousand, seven hundred twelve".