406684800 has 288 divisors, whose sum is σ = 1507768080. Its totient is φ = 108241920.

The previous prime is 406684799. The next prime is 406684807. The reversal of 406684800 is 8486604.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (406684807) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 777339 + ... + 777861.

Almost surely, 2^406684800 is an apocalyptic number.

406684800 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 406684800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (753884040).

406684800 is an abundant number, since it is smaller than the sum of its proper divisors (1101083280).

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

406684800 is an equidigital number, since it uses as much as digits as its factorization.

406684800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 562 (or 533 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 36.

The square root of 406684800 is about 20166.4275467917. The cubic root of 406684800 is about 740.8881471582. Note that the first 3 decimals are identical.

The spelling of 406684800 in words is "four hundred six million, six hundred eighty-four thousand, eight hundred".