409944 has 64 divisors (see below), whose sum is σ = 1152000. Its totient is φ = 120960.

The previous prime is 409943. The next prime is 409951. The reversal of 409944 is 449904.

It is a hoax number, since the sum of its digits (30) coincides with the sum of the digits of its distinct prime factors.

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 409944.

It is not an unprimeable number, because it can be changed into a prime (409943) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 13209 + ... + 13239.

It is an arithmetic number, because the mean of its divisors is an integer number (18000).

2⁴⁰⁹⁹⁴⁴ 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 409944, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (576000).

409944 is an abundant number, since it is smaller than the sum of its proper divisors (742056).

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

409944 is a wasteful number, since it uses less digits than its factorization.

409944 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 88 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 5184, while the sum is 30.

The square root of 409944 is about 640.2686935967. The cubic root of 409944 is about 74.2862059703.

Multiplying 409944 by its sum of digits (30), we get a triangular number (12298320 = T₄₉₅₉).

The spelling of 409944 in words is "four hundred nine thousand, nine hundred forty-four".