409864000 has 224 divisors, whose sum is σ = 1251484416. Its totient is φ = 129484800.

The previous prime is 409863977. The next prime is 409864001. The reversal of 409864000 is 468904.

It is a tau number, because it is divible by the number of its divisors (224).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (409864001) by changing a digit.

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 31 ways as a sum of consecutive naturals, for example, 727719 + ... + 728281.

It is an arithmetic number, because the mean of its divisors is an integer number (5586984).

Almost surely, 2^409864000 is an apocalyptic number.

409864000 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 409864000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (625742208).

409864000 is an abundant number, since it is smaller than the sum of its proper divisors (841620416).

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

409864000 is a wasteful number, since it uses less digits than its factorization.

409864000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 610 (or 590 counting only the distinct ones).

The product of its (nonzero) digits is 6912, while the sum is 31.

The square root of 409864000 is about 20245.0981721502. The cubic root of 409864000 is about 742.8137337272.

The spelling of 409864000 in words is "four hundred nine million, eight hundred sixty-four thousand".