408928800 has 288 divisors, whose sum is σ = 1542651264. Its totient is φ = 92160000.

The previous prime is 408928783. The next prime is 408928813. The reversal of 408928800 is 8829804.

It is a happy number.

It is a Smith number, since the sum of its digits (39) coincides with the sum of the digits of its prime factors.

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, 1696680 + ... + 1696920.

It is an arithmetic number, because the mean of its divisors is an integer number (5356428).

Almost surely, 2^408928800 is an apocalyptic number.

408928800 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 408928800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (771325632).

408928800 is an abundant number, since it is smaller than the sum of its proper divisors (1133722464).

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

408928800 is a wasteful number, since it uses less digits than its factorization.

408928800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 372 (or 359 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 39.

The square root of 408928800 is about 20221.9880328320. The cubic root of 408928800 is about 742.2483360732.

The spelling of 408928800 in words is "four hundred eight million, nine hundred twenty-eight thousand, eight hundred".