409046547792960 has 8064 divisors, whose sum is σ = 2027499653716992. Its totient is φ = 76517631590400.

The previous prime is 409046547792937. The next prime is 409046547792989. The reversal of 409046547792960 is 69297745640904.

It is a happy number.

409046547792960 is a `hidden beast` number, since 4 + 0 + 9 + 0 + 4 + 6 + 5 + 477 + 92 + 9 + 60 = 666.

It is a super-3 number, since 3×409046547792960³ (a number of 45 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 1151 ways as a sum of consecutive naturals, for example, 3619880953864 + ... + 3619880953976.

It is an arithmetic number, because the mean of its divisors is an integer number (251426048328).

Almost surely, 2^{409046547792960} is an apocalyptic number.

409046547792960 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 409046547792960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1013749826858496).

409046547792960 is an abundant number, since it is smaller than the sum of its proper divisors (1618453105924032).

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

409046547792960 is a wasteful number, since it uses less digits than its factorization.

409046547792960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 305 (or 272 counting only the distinct ones).

The product of its (nonzero) digits is 823011840, while the sum is 72.

The spelling of 409046547792960 in words is "four hundred nine trillion, forty-six billion, five hundred forty-seven million, seven hundred ninety-two thousand, nine hundred sixty".