413642319560800 has 144 divisors (see below), whose sum is σ = 1101871727695872. Its totient is φ = 150378929062400.

The previous prime is 413642319560797. The next prime is 413642319560807. The reversal of 413642319560800 is 8065913246314.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413642319560807) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 30622809 + ... + 42012391.

It is an arithmetic number, because the mean of its divisors is an integer number (7651886997888).

Almost surely, 2^{413642319560800} is an apocalyptic number.

413642319560800 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 413642319560800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (550935863847936).

413642319560800 is an abundant number, since it is smaller than the sum of its proper divisors (688229408135072).

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

413642319560800 is a wasteful number, since it uses less digits than its factorization.

413642319560800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 11393741 (or 11393728 counting only the distinct ones).

The product of its (nonzero) digits is 3732480, while the sum is 52.

The spelling of 413642319560800 in words is "four hundred thirteen trillion, six hundred forty-two billion, three hundred nineteen million, five hundred sixty thousand, eight hundred".