34540138234800 has 720 divisors, whose sum is σ = 132194729472000. Its totient is φ = 8281937664000.

The previous prime is 34540138234741. The next prime is 34540138234871. The reversal of 34540138234800 is 843283104543.

34540138234800 is a `hidden beast` number, since 3 + 4 + 5 + 401 + 3 + 8 + 234 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×34540138234800² (a number of 28 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 1664654826 + ... + 1664675574.

Almost surely, 2^{34540138234800} is an apocalyptic number.

34540138234800 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 34540138234800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (66097364736000).

34540138234800 is an abundant number, since it is smaller than the sum of its proper divisors (97654591237200).

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

34540138234800 is a wasteful number, since it uses less digits than its factorization.

34540138234800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 21242 (or 21228 counting only the distinct ones).

The product of its (nonzero) digits is 1105920, while the sum is 45.

The spelling of 34540138234800 in words is "thirty-four trillion, five hundred forty billion, one hundred thirty-eight million, two hundred thirty-four thousand, eight hundred".