509040 has 120 divisors (see below), whose sum is σ = 1973088. Its totient is φ = 115200.

The previous prime is 509027. The next prime is 509053. The reversal of 509040 is 40905.

It is an interprime number because it is at equal distance from previous prime (509027) and next prime (509053).

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 4990 + ... + 5090.

2⁵⁰⁹⁰⁴⁰ 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 509040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (986544).

509040 is an abundant number, since it is smaller than the sum of its proper divisors (1464048).

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

509040 is a wasteful number, since it uses less digits than its factorization.

509040 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 127 (or 118 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 18.

The square root of 509040 is about 713.4703918173. The cubic root of 509040 is about 79.8455352834.

Adding to 509040 its reverse (40905), we get a palindrome (549945).

The spelling of 509040 in words is "five hundred nine thousand, forty".