408288000 has 144 divisors (see below), whose sum is σ = 1356447456. Its totient is φ = 108851200.

The previous prime is 408287989. The next prime is 408288043. The reversal of 408288000 is 882804.

It is a Harshad number since it is a multiple of its sum of digits (30).

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 15 ways as a sum of consecutive naturals, for example, 93874 + ... + 98126.

It is an arithmetic number, because the mean of its divisors is an integer number (9419774).

Almost surely, 2^408288000 is an apocalyptic number.

408288000 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 408288000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (678223728).

408288000 is an abundant number, since it is smaller than the sum of its proper divisors (948159456).

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

408288000 is an equidigital number, since it uses as much as digits as its factorization.

408288000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4287 (or 4263 counting only the distinct ones).

The product of its (nonzero) digits is 4096, while the sum is 30.

The square root of 408288000 is about 20206.1376814076. The cubic root of 408288000 is about 741.8604271492.

It can be divided in two parts, 40828 and 8000, that added together give a triangular number (48828 = T₃₁₂).

The spelling of 408288000 in words is "four hundred eight million, two hundred eighty-eight thousand".