34561380188160 has 576 divisors, whose sum is σ = 140439861676800. Its totient is φ = 7899715731456.

The previous prime is 34561380188123. The next prime is 34561380188191. The reversal of 34561380188160 is 6188108316543.

It is a happy number.

34561380188160 is a `hidden beast` number, since 3 + 4 + 5 + 613 + 8 + 0 + 1 + 8 + 8 + 16 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (576).

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

It is a junction number, because it is equal to n+sod(n) for n = 34561380188097 and 34561380188106.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 123723526 + ... + 124002554.

It is an arithmetic number, because the mean of its divisors is an integer number (243819204300).

Almost surely, 2^{34561380188160} is an apocalyptic number.

34561380188160 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 34561380188160, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (70219930838400).

34561380188160 is an abundant number, since it is smaller than the sum of its proper divisors (105878481488640).

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

34561380188160 is an frugal number, since it uses more digits than its factorization.

34561380188160 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 279084 (or 279046 counting only the distinct ones).

The product of its (nonzero) digits is 3317760, while the sum is 54.

The spelling of 34561380188160 in words is "thirty-four trillion, five hundred sixty-one billion, three hundred eighty million, one hundred eighty-eight thousand, one hundred sixty".