409598560800 has 1728 divisors, whose sum is σ = 1800046789632. Its totient is φ = 86261760000.

The previous prime is 409598560799. The next prime is 409598560807. The reversal of 409598560800 is 8065895904.

It is a happy number.

409598560800 is a `hidden beast` number, since 40 + 9 + 598 + 5 + 6 + 0 + 8 + 0 + 0 = 666.

409598560800 is digitally balanced in base 4, because in such base it contains all the possibile digits an equal number of times.

It is not an unprimeable number, because it can be changed into a prime (409598560807) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 1308621444 + ... + 1308621756.

It is an arithmetic number, because the mean of its divisors is an integer number (1041693744).

Almost surely, 2^409598560800 is an apocalyptic number.

409598560800 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 409598560800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (900023394816).

409598560800 is an abundant number, since it is smaller than the sum of its proper divisors (1390448228832).

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

409598560800 is a wasteful number, since it uses less digits than its factorization.

409598560800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 435 (or 419 counting only the distinct ones).

The product of its (nonzero) digits is 3110400, while the sum is 54.

The spelling of 409598560800 in words is "four hundred nine billion, five hundred ninety-eight million, five hundred sixty thousand, eight hundred".