105609100788072 has 1280 divisors, whose sum is σ = 384788828160000. Its totient is φ = 26358527416320.

The previous prime is 105609100788071. The next prime is 105609100788109. The reversal of 105609100788072 is 270887001906501.

105609100788072 is a `hidden beast` number, since 1 + 0 + 560 + 9 + 1 + 0 + 0 + 7 + 8 + 8 + 0 + 72 = 666.

It is a super-2 number, since 2×105609100788072² (a number of 29 digits) contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (105609100788071) by changing a digit.

It is a polite number, since it can be written in 319 ways as a sum of consecutive naturals, for example, 16529829454 + ... + 16529835842.

It is an arithmetic number, because the mean of its divisors is an integer number (300616272000).

Almost surely, 2^{105609100788072} is an apocalyptic number.

105609100788072 is a gapful number since it is divisible by the number (12) 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 105609100788072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (192394414080000).

105609100788072 is an abundant number, since it is smaller than the sum of its proper divisors (279179727371928).

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

105609100788072 is a wasteful number, since it uses less digits than its factorization.

105609100788072 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 6756 (or 6743 counting only the distinct ones).

The product of its (nonzero) digits is 1693440, while the sum is 54.

The spelling of 105609100788072 in words is "one hundred five trillion, six hundred nine billion, one hundred million, seven hundred eighty-eight thousand, seventy-two".