409448000 has 224 divisors, whose sum is σ = 1136099328. Its totient is φ = 145152000.

The previous prime is 409447981. The next prime is 409448027. The reversal of 409448000 is 844904.

It is a happy number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 3223937 + ... + 3224063.

It is an arithmetic number, because the mean of its divisors is an integer number (5071872).

Almost surely, 2^409448000 is an apocalyptic number.

409448000 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 409448000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (568049664).

409448000 is an abundant number, since it is smaller than the sum of its proper divisors (726651328).

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

409448000 is a wasteful number, since it uses less digits than its factorization.

409448000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 198 (or 178 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 29.

The square root of 409448000 is about 20234.8214719083. The cubic root of 409448000 is about 742.5623372332.

The spelling of 409448000 in words is "four hundred nine million, four hundred forty-eight thousand".