409584 has 80 divisors (see below), whose sum is σ = 1285632. Its totient is φ = 109824.

The previous prime is 409579. The next prime is 409589. The reversal of 409584 is 485904.

It is an interprime number because it is at equal distance from previous prime (409579) and next prime (409589).

It is a zygodrome in base 2.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 409584.

It is not an unprimeable number, because it can be changed into a prime (409589) 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, 7702 + ... + 7754.

2⁴⁰⁹⁵⁸⁴ 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 409584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (642816).

409584 is an abundant number, since it is smaller than the sum of its proper divisors (876048).

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

409584 is a wasteful number, since it uses less digits than its factorization.

409584 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 94 (or 88 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 30.

The square root of 409584 is about 639.9874998779. The cubic root of 409584 is about 74.2644543275.

The spelling of 409584 in words is "four hundred nine thousand, five hundred eighty-four".