414401944320 has 2304 divisors, whose sum is σ = 2005629050880. Its totient is φ = 78479622144.

The previous prime is 414401944291. The next prime is 414401944379. The reversal of 414401944320 is 23449104414.

It is a happy number.

414401944320 is a `hidden beast` number, since 4 + 1 + 440 + 194 + 4 + 3 + 20 = 666.

It is a tau number, because it is divible by the number of its divisors (2304).

It is a super-4 number, since 4×414401944320⁴ (a number of 48 digits) contains 4444 as substring.

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 255 ways as a sum of consecutive naturals, for example, 1229679192 + ... + 1229679528.

It is an arithmetic number, because the mean of its divisors is an integer number (870498720).

Almost surely, 2^414401944320 is an apocalyptic number.

414401944320 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 414401944320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1002814525440).

414401944320 is an abundant number, since it is smaller than the sum of its proper divisors (1591227106560).

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

414401944320 is a wasteful number, since it uses less digits than its factorization.

414401944320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 427 (or 407 counting only the distinct ones).

The product of its (nonzero) digits is 55296, while the sum is 36.

The spelling of 414401944320 in words is "four hundred fourteen billion, four hundred one million, nine hundred forty-four thousand, three hundred twenty".