34125993921600 has 1344 divisors, whose sum is σ = 147021916979200. Its totient is φ = 7535130624000.

The previous prime is 34125993921587. The next prime is 34125993921647. The reversal of 34125993921600 is 612939952143.

34125993921600 is a `hidden beast` number, since 3 + 4 + 1 + 2 + 5 + 9 + 9 + 3 + 9 + 21 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1344).

It is a super-2 number, since 2×34125993921600² (a number of 28 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

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, 5802750660 + ... + 5802756540.

Almost surely, 2^{34125993921600} is an apocalyptic number.

34125993921600 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 34125993921600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (73510958489600).

34125993921600 is an abundant number, since it is smaller than the sum of its proper divisors (112895923057600).

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

34125993921600 is a wasteful number, since it uses less digits than its factorization.

34125993921600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 6569 (or 6548 counting only the distinct ones).

The product of its (nonzero) digits is 3149280, while the sum is 54.

The spelling of 34125993921600 in words is "thirty-four trillion, one hundred twenty-five billion, nine hundred ninety-three million, nine hundred twenty-one thousand, six hundred".