34349546016000 has 1728 divisors, whose sum is σ = 133406320320000. Its totient is φ = 8693559705600.

The previous prime is 34349546015977. The next prime is 34349546016041. The reversal of 34349546016000 is 61064594343.

34349546016000 is a `hidden beast` number, since 3 + 4 + 3 + 49 + 546 + 0 + 1 + 60 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1728).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

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, 172610783901 + ... + 172610784099.

Almost surely, 2^{34349546016000} is an apocalyptic number.

34349546016000 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 34349546016000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (66703160160000).

34349546016000 is an abundant number, since it is smaller than the sum of its proper divisors (99056774304000).

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

34349546016000 is an equidigital number, since it uses as much as digits as its factorization.

34349546016000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 434 (or 321 counting only the distinct ones).

The product of its (nonzero) digits is 933120, while the sum is 45.

The spelling of 34349546016000 in words is "thirty-four trillion, three hundred forty-nine billion, five hundred forty-six million, sixteen thousand".