2305106311680 has 640 divisors, whose sum is σ = 8341983936000. Its totient is φ = 603213004800.

The previous prime is 2305106311603. The next prime is 2305106311681. The reversal of 2305106311680 is 861136015032.

2305106311680 is a `hidden beast` number, since 2 + 3 + 0 + 5 + 1 + 0 + 631 + 16 + 8 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (640).

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

It is not an unprimeable number, because it can be changed into a prime (2305106311681) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 1182711346 + ... + 1182713294.

It is an arithmetic number, because the mean of its divisors is an integer number (13034349900).

Almost surely, 2^{2305106311680} is an apocalyptic number.

2305106311680 is a gapful number since it is divisible by the number (20) 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 2305106311680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4170991968000).

2305106311680 is an abundant number, since it is smaller than the sum of its proper divisors (6036877624320).

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

2305106311680 is a wasteful number, since it uses less digits than its factorization.

2305106311680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2293 (or 2271 counting only the distinct ones).

The product of its (nonzero) digits is 25920, while the sum is 36.

The spelling of 2305106311680 in words is "two trillion, three hundred five billion, one hundred six million, three hundred eleven thousand, six hundred eighty".