406348800 has 528 divisors, whose sum is σ = 1620437952. Its totient is φ = 88473600.

The previous prime is 406348799. The next prime is 406348823. The reversal of 406348800 is 8843604.

It is a tau number, because it is divible by the number of its divisors (528).

It is a super-2 number, since 2×406348800² = 330238694522880000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (33).

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, 10982382 + ... + 10982418.

Almost surely, 2^406348800 is an apocalyptic number.

406348800 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 406348800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (810218976).

406348800 is an abundant number, since it is smaller than the sum of its proper divisors (1214089152).

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

406348800 is a wasteful number, since it uses less digits than its factorization.

406348800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 94 (or 71 counting only the distinct ones).

The product of its (nonzero) digits is 18432, while the sum is 33.

The square root of 406348800 is about 20158.0951481037. The cubic root of 406348800 is about 740.6840521556.

The spelling of 406348800 in words is "four hundred six million, three hundred forty-eight thousand, eight hundred".