414006448400 has 120 divisors (see below), whose sum is σ = 999415129320. Its totient is φ = 164811243520.

The previous prime is 414006448397. The next prime is 414006448421. The reversal of 414006448400 is 4844600414.

It can be written as a sum of positive squares in 12 ways, for example, as 171359569936 + 242646878464 = 413956^2 + 492592^2 .

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 23 ways as a sum of consecutive naturals, for example, 80340224 + ... + 80345376.

It is an arithmetic number, because the mean of its divisors is an integer number (8328459411).

Almost surely, 2^414006448400 is an apocalyptic number.

414006448400 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 414006448400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (499707564660).

414006448400 is an abundant number, since it is smaller than the sum of its proper divisors (585408680920).

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

414006448400 is a wasteful number, since it uses less digits than its factorization.

414006448400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 6093 (or 6082 counting only the distinct ones).

The product of its (nonzero) digits is 49152, while the sum is 35.

The spelling of 414006448400 in words is "four hundred fourteen billion, six million, four hundred forty-eight thousand, four hundred".