509680 has 40 divisors (see below), whose sum is σ = 1240992. Its totient is φ = 194304.

The previous prime is 509659. The next prime is 509681. The reversal of 509680 is 86905.

509680 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (40).

It is a hoax number, since the sum of its digits (28) coincides with the sum of the digits of its distinct prime factors.

It is a congruent number.

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

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1702 + ... + 1978.

2⁵⁰⁹⁶⁸⁰ 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 509680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (620496).

509680 is an abundant number, since it is smaller than the sum of its proper divisors (731312).

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

509680 is a wasteful number, since it uses less digits than its factorization.

509680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 313 (or 307 counting only the distinct ones).

The product of its (nonzero) digits is 2160, while the sum is 28.

The square root of 509680 is about 713.9187628855. The cubic root of 509680 is about 79.8789836972.

It can be divided in two parts, 50 and 9680, that added together give a triangular number (9730 = T₁₃₉).

The spelling of 509680 in words is "five hundred nine thousand, six hundred eighty".