413365824000 has 960 divisors, whose sum is σ = 1586355788160. Its totient is φ = 103160217600.

The previous prime is 413365823977. The next prime is 413365824007. The reversal of 413365824000 is 428563314.

413365824000 is a `hidden beast` number, since 4 + 1 + 3 + 36 + 582 + 40 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (960).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (413365824007) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1171007824 + ... + 1171008176.

It is an arithmetic number, because the mean of its divisors is an integer number (1652453946).

Almost surely, 2^413365824000 is an apocalyptic number.

413365824000 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 413365824000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (793177894080).

413365824000 is an abundant number, since it is smaller than the sum of its proper divisors (1172989964160).

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

413365824000 is a wasteful number, since it uses less digits than its factorization.

413365824000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 518 (or 489 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 36.

The spelling of 413365824000 in words is "four hundred thirteen billion, three hundred sixty-five million, eight hundred twenty-four thousand".