414213444400 has 360 divisors, whose sum is σ = 1246934863680. Its totient is φ = 131407557120.

The previous prime is 414213444391. The next prime is 414213444413. The reversal of 414213444400 is 4444312414.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 16000267 + ... + 16026133.

Almost surely, 2^414213444400 is an apocalyptic number.

414213444400 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 414213444400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (623467431840).

414213444400 is an abundant number, since it is smaller than the sum of its proper divisors (832721419280).

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

414213444400 is a wasteful number, since it uses less digits than its factorization.

414213444400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 25961 (or 25943 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 31.

Adding to 414213444400 its reverse (4444312414), we get a palindrome (418657756814).

The spelling of 414213444400 in words is "four hundred fourteen billion, two hundred thirteen million, four hundred forty-four thousand, four hundred".