105188166720 has 672 divisors, whose sum is σ = 454439731200. Its totient is φ = 22190837760.

The previous prime is 105188166659. The next prime is 105188166737. The reversal of 105188166720 is 27661881501.

105188166720 is a `hidden beast` number, since 1 + 0 + 518 + 8 + 1 + 66 + 72 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (672).

It is a super-2 number, since 2×105188166720² (a number of 23 digits) contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 12837825 + ... + 12846015.

It is an arithmetic number, because the mean of its divisors is an integer number (676249600).

Almost surely, 2^105188166720 is an apocalyptic number.

105188166720 is a gapful number since it is divisible by the number (10) 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 105188166720, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (227219865600).

105188166720 is an abundant number, since it is smaller than the sum of its proper divisors (349251564480).

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

105188166720 is a wasteful number, since it uses less digits than its factorization.

105188166720 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 8248 (or 8221 counting only the distinct ones).

The product of its (nonzero) digits is 161280, while the sum is 45.

The spelling of 105188166720 in words is "one hundred five billion, one hundred eighty-eight million, one hundred sixty-six thousand, seven hundred twenty".