408096000 has 432 divisors, whose sum is σ = 1595914320. Its totient is φ = 99532800.

The previous prime is 408095993. The next prime is 408096023. The reversal of 408096000 is 690804.

It can be written as a sum of positive squares in 8 ways, for example, as 169208064 + 238887936 = 13008^2 + 15456^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3743946 + ... + 3744054.

Almost surely, 2^408096000 is an apocalyptic number.

408096000 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 408096000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (797957160).

408096000 is an abundant number, since it is smaller than the sum of its proper divisors (1187818320).

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

408096000 is a wasteful number, since it uses less digits than its factorization.

408096000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 159 (or 132 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 408096000 is about 20201.3860910582. The cubic root of 408096000 is about 741.7441207387.

The spelling of 408096000 in words is "four hundred eight million, ninety-six thousand".