406408000 has 112 divisors (see below), whose sum is σ = 1034424144. Its totient is φ = 158054400.

The previous prime is 406407979. The next prime is 406408019. The reversal of 406408000 is 804604.

It can be written as a sum of positive squares in 8 ways, for example, as 627264 + 405780736 = 792^2 + 20144^2 .

It is a congruent number.

It is an unprimeable number.

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 15 ways as a sum of consecutive naturals, for example, 295314 + ... + 296686.

Almost surely, 2^406408000 is an apocalyptic number.

406408000 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 406408000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (517212072).

406408000 is an abundant number, since it is smaller than the sum of its proper divisors (628016144).

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

406408000 is a wasteful number, since it uses less digits than its factorization.

406408000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1437 (or 1417 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 22.

The square root of 406408000 is about 20159.5634873377. The cubic root of 406408000 is about 740.7200199142.

The spelling of 406408000 in words is "four hundred six million, four hundred eight thousand".