509820 has 48 divisors (see below), whose sum is σ = 1481760. Its totient is φ = 130816.

The previous prime is 509801. The next prime is 509833. The reversal of 509820 is 28905.

It is a congruent number.

It is an unprimeable number.

509820 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1594 + ... + 1886.

It is an arithmetic number, because the mean of its divisors is an integer number (30870).

2⁵⁰⁹⁸²⁰ 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 509820, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (740880).

509820 is an abundant number, since it is smaller than the sum of its proper divisors (971940).

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

509820 is a wasteful number, since it uses less digits than its factorization.

509820 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 334 (or 332 counting only the distinct ones).

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

The square root of 509820 is about 714.0168065249. The cubic root of 509820 is about 79.8862968047.

Subtracting from 509820 its sum of digits (24), we obtain a square (509796 = 714²).

It can be divided in two parts, 50 and 9820, that added together give a triangular number (9870 = T₁₄₀).

The spelling of 509820 in words is "five hundred nine thousand, eight hundred twenty".