414020204400 has 240 divisors, whose sum is σ = 1471337435520. Its totient is φ = 98667187200.

The previous prime is 414020204369. The next prime is 414020204443. The reversal of 414020204400 is 4402020414.

It is a tau number, because it is divible by the number of its divisors (240).

It is a congruent number.

It is an unprimeable number.

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 47 ways as a sum of consecutive naturals, for example, 512994 + ... + 1044606.

It is an arithmetic number, because the mean of its divisors is an integer number (6130572648).

Almost surely, 2^414020204400 is an apocalyptic number.

414020204400 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 414020204400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (735668717760).

414020204400 is an abundant number, since it is smaller than the sum of its proper divisors (1057317231120).

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

414020204400 is a wasteful number, since it uses less digits than its factorization.

414020204400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 531704 (or 531693 counting only the distinct ones).

The product of its (nonzero) digits is 1024, while the sum is 21.

Adding to 414020204400 its reverse (4402020414), we get a palindrome (418422224814).

The spelling of 414020204400 in words is "four hundred fourteen billion, twenty million, two hundred four thousand, four hundred".