509640 has 64 divisors (see below), whose sum is σ = 1589760. Its totient is φ = 130560.

The previous prime is 509633. The next prime is 509647. The reversal of 509640 is 46905.

It is an interprime number because it is at equal distance from previous prime (509633) and next prime (509647).

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

It is a self number, because there is not a number n which added to its sum of digits gives 509640.

It is not an unprimeable number, because it can be changed into a prime (509647) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 3652 + ... + 3788.

It is an arithmetic number, because the mean of its divisors is an integer number (24840).

2⁵⁰⁹⁶⁴⁰ 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 509640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (794880).

509640 is an abundant number, since it is smaller than the sum of its proper divisors (1080120).

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

509640 is a wasteful number, since it uses less digits than its factorization.

509640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 182 (or 178 counting only the distinct ones).

The product of its (nonzero) digits is 1080, while the sum is 24.

The square root of 509640 is about 713.8907479440. The cubic root of 509640 is about 79.8768939919.

The spelling of 509640 in words is "five hundred nine thousand, six hundred forty".