413744218272 has 960 divisors, whose sum is σ = 1607050368000. Its totient is φ = 101583175680.

The previous prime is 413744218189. The next prime is 413744218289. The reversal of 413744218272 is 272812447314.

413744218272 is a `hidden beast` number, since 4 + 1 + 374 + 4 + 2 + 1 + 8 + 272 = 666.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an unprimeable number.

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 159 ways as a sum of consecutive naturals, for example, 921479104 + ... + 921479552.

It is an arithmetic number, because the mean of its divisors is an integer number (1674010800).

Almost surely, 2^413744218272 is an apocalyptic number.

413744218272 is a gapful number since it is divisible by the number (42) 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 413744218272, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (803525184000).

413744218272 is an abundant number, since it is smaller than the sum of its proper divisors (1193306149728).

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

413744218272 is an equidigital number, since it uses as much as digits as its factorization.

413744218272 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 523 (or 491 counting only the distinct ones).

The product of its digits is 602112, while the sum is 45.

The spelling of 413744218272 in words is "four hundred thirteen billion, seven hundred forty-four million, two hundred eighteen thousand, two hundred seventy-two".