409904 has 40 divisors (see below), whose sum is σ = 924048. Its totient is φ = 174080.

The previous prime is 409901. The next prime is 409909.

409904 is nontrivially palindromic in base 10.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (409901) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2924 + ... + 3060.

2⁴⁰⁹⁹⁰⁴ is an apocalyptic number.

409904 is a gapful number since it is divisible by the number (44) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 409904, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (462024).

409904 is an abundant number, since it is smaller than the sum of its proper divisors (514144).

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

409904 is a wasteful number, since it uses less digits than its factorization.

409904 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 173 (or 167 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 26.

The square root of 409904 is about 640.2374559490. The cubic root of 409904 is about 74.2837897501.

The spelling of 409904 in words is "four hundred nine thousand, nine hundred four".