34412378112000 has 2880 divisors, whose sum is σ = 155592143965440. Its totient is φ = 7134511104000.

The previous prime is 34412378111999. The next prime is 34412378112019. The reversal of 34412378112000 is 21187321443.

34412378112000 is a `hidden beast` number, since 3 + 4 + 412 + 37 + 8 + 1 + 1 + 200 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2880).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 63608831730 + ... + 63608832270.

It is an arithmetic number, because the mean of its divisors is an integer number (54025049988).

Almost surely, 2^{34412378112000} is an apocalyptic number.

34412378112000 is a gapful number since it is divisible by the number (30) 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 34412378112000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (77796071982720).

34412378112000 is an abundant number, since it is smaller than the sum of its proper divisors (121179765853440).

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

34412378112000 is a wasteful number, since it uses less digits than its factorization.

34412378112000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 643 (or 604 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The spelling of 34412378112000 in words is "thirty-four trillion, four hundred twelve billion, three hundred seventy-eight million, one hundred twelve thousand".