34406072064000 has 4608 divisors, whose sum is σ = 165747726144000. Its totient is φ = 6797603635200.

The previous prime is 34406072063989. The next prime is 34406072064061. The reversal of 34406072064000 is 46027060443.

34406072064000 is a `hidden beast` number, since 3 + 4 + 4 + 0 + 6 + 0 + 7 + 2 + 0 + 640 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (4608).

It is a super-2 number, since 2×34406072064000² (a number of 28 digits) contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 174650111902 + ... + 174650112098.

It is an arithmetic number, because the mean of its divisors is an integer number (35969558625).

Almost surely, 2^{34406072064000} is an apocalyptic number.

34406072064000 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 34406072064000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (82873863072000).

34406072064000 is an abundant number, since it is smaller than the sum of its proper divisors (131341654080000).

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

34406072064000 is a wasteful number, since it uses less digits than its factorization.

34406072064000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 291 (or 244 counting only the distinct ones).

The product of its (nonzero) digits is 96768, while the sum is 36.

The spelling of 34406072064000 in words is "thirty-four trillion, four hundred six billion, seventy-two million, sixty-four thousand".