414112344012000 has 576 divisors, whose sum is σ = 1474137137753280. Its totient is φ = 110095759872000.

The previous prime is 414112344011981. The next prime is 414112344012011. The reversal of 414112344012000 is 210443211414.

414112344012000 is a `hidden beast` number, since 4 + 1 + 4 + 1 + 1 + 234 + 401 + 20 + 0 + 0 = 666.

It is a super-2 number, since 2×414112344012000² (a number of 30 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 25659099931 + ... + 25659116069.

It is an arithmetic number, because the mean of its divisors is an integer number (2559265864155).

Almost surely, 2^{414112344012000} is an apocalyptic number.

414112344012000 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 414112344012000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (737068568876640).

414112344012000 is an abundant number, since it is smaller than the sum of its proper divisors (1060024793741280).

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

414112344012000 is a wasteful number, since it uses less digits than its factorization.

414112344012000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 18284 (or 18263 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

Adding to 414112344012000 its reverse (210443211414), we get a palindrome (414322787223414).

The spelling of 414112344012000 in words is "four hundred fourteen trillion, one hundred twelve billion, three hundred forty-four million, twelve thousand".