413140464000 has 1152 divisors, whose sum is σ = 1652361590880. Its totient is φ = 98841600000.

The previous prime is 413140463903. The next prime is 413140464001. The reversal of 413140464000 is 464041314.

413140464000 is a `hidden beast` number, since 4 + 1 + 3 + 14 + 0 + 4 + 640 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413140464001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 2282543910 + ... + 2282544090.

Almost surely, 2^413140464000 is an apocalyptic number.

413140464000 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 413140464000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (826180795440).

413140464000 is an abundant number, since it is smaller than the sum of its proper divisors (1239221126880).

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

413140464000 is a wasteful number, since it uses less digits than its factorization.

413140464000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 369 (or 333 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

The spelling of 413140464000 in words is "four hundred thirteen billion, one hundred forty million, four hundred sixty-four thousand".