406540800 has 180 divisors, whose sum is σ = 1455309570. Its totient is φ = 108380160.

The previous prime is 406540781. The next prime is 406540811. The reversal of 406540800 is 8045604.

406540800 is a `hidden beast` number, since 4 + 0 + 654 + 0 + 8 + 0 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 208744704 + 197796096 = 14448^2 + 14064^2 .

It is a tau number, because it is divible by the number of its divisors (180).

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 113436 + ... + 116964.

Almost surely, 2^406540800 is an apocalyptic number.

406540800 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 406540800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (727654785).

406540800 is an abundant number, since it is smaller than the sum of its proper divisors (1048768770).

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

406540800 is a wasteful number, since it uses less digits than its factorization.

406540800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3563 (or 3539 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 406540800 is about 20162.8569404239. The cubic root of 406540800 is about 740.8006916416.

The spelling of 406540800 in words is "four hundred six million, five hundred forty thousand, eight hundred".