413990120980800 has 3024 divisors, whose sum is σ = 1887524450203392. Its totient is φ = 85262517043200.

The previous prime is 413990120980759. The next prime is 413990120980817. The reversal of 413990120980800 is 8089021099314.

413990120980800 is a `hidden beast` number, since 41 + 399 + 0 + 1 + 209 + 8 + 0 + 8 + 0 + 0 = 666.

It is a congruent number.

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 431 ways as a sum of consecutive naturals, for example, 198747056559 + ... + 198747058641.

It is an arithmetic number, because the mean of its divisors is an integer number (624181365808).

Almost surely, 2^{413990120980800} is an apocalyptic number.

413990120980800 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 413990120980800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (943762225101696).

413990120980800 is an abundant number, since it is smaller than the sum of its proper divisors (1473534329222592).

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

413990120980800 is a wasteful number, since it uses less digits than its factorization.

413990120980800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2646 (or 2621 counting only the distinct ones).

The product of its (nonzero) digits is 1119744, while the sum is 54.

The spelling of 413990120980800 in words is "four hundred thirteen trillion, nine hundred ninety billion, one hundred twenty million, nine hundred eighty thousand, eight hundred".