413354224144000 has 512 divisors, whose sum is σ = 1080743116377600. Its totient is φ = 157004660736000.

The previous prime is 413354224143929. The next prime is 413354224144003. The reversal of 413354224144000 is 441422453314.

It is a happy number.

It is not an unprimeable number, because it can be changed into a prime (413354224144003) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 19927397629 + ... + 19927418371.

It is an arithmetic number, because the mean of its divisors is an integer number (2110826399175).

Almost surely, 2^{413354224144000} is an apocalyptic number.

413354224144000 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 413354224144000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (540371558188800).

413354224144000 is an abundant number, since it is smaller than the sum of its proper divisors (667388892233600).

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

413354224144000 is a wasteful number, since it uses less digits than its factorization.

413354224144000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 21509 (or 21487 counting only the distinct ones).

The product of its (nonzero) digits is 184320, while the sum is 37.

Adding to 413354224144000 its reverse (441422453314), we get a palindrome (413795646597314).

The spelling of 413354224144000 in words is "four hundred thirteen trillion, three hundred fifty-four billion, two hundred twenty-four million, one hundred forty-four thousand".