409400 has 48 divisors (see below), whose sum is σ = 1004400. Its totient is φ = 154880.

The previous prime is 409397. The next prime is 409429. The reversal of 409400 is 4904.

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 409400.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4556 + ... + 4644.

It is an arithmetic number, because the mean of its divisors is an integer number (20925).

2⁴⁰⁹⁴⁰⁰ is an apocalyptic number.

409400 is a gapful number since it is divisible by the number (40) 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 409400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (502200).

409400 is an abundant number, since it is smaller than the sum of its proper divisors (595000).

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

409400 is a wasteful number, since it uses less digits than its factorization.

409400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 119 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 17.

The square root of 409400 is about 639.8437309219. The cubic root of 409400 is about 74.2533318990.

Subtracting from 409400 its reverse (4904), we obtain a square (404496 = 636²).

The spelling of 409400 in words is "four hundred nine thousand, four hundred".