414200413003344 has 320 divisors, whose sum is σ = 1199507306618880. Its totient is φ = 122084631900160.

The previous prime is 414200413003319. The next prime is 414200413003387. The reversal of 414200413003344 is 443300314002414.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 38164595422 + ... + 38164606274.

It is an arithmetic number, because the mean of its divisors is an integer number (3748460333184).

Almost surely, 2^{414200413003344} is an apocalyptic number.

414200413003344 is a gapful number since it is divisible by the number (44) 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 414200413003344, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (599753653309440).

414200413003344 is an abundant number, since it is smaller than the sum of its proper divisors (785306893615536).

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

414200413003344 is a wasteful number, since it uses less digits than its factorization.

414200413003344 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 20298 (or 20292 counting only the distinct ones).

The product of its (nonzero) digits is 55296, while the sum is 33.

Adding to 414200413003344 its reverse (443300314002414), we get a palindrome (857500727005758).

The spelling of 414200413003344 in words is "four hundred fourteen trillion, two hundred billion, four hundred thirteen million, three thousand, three hundred forty-four".