105688728000 has 672 divisors, whose sum is σ = 405743420160. Its totient is φ = 26166067200.

The previous prime is 105688727987. The next prime is 105688728011. The reversal of 105688728000 is 827886501.

105688728000 is a `hidden beast` number, since 1 + 0 + 568 + 8 + 7 + 2 + 80 + 0 + 0 = 666.

It is a super-2 number, since 2×105688728000² (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 pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 96695454 + ... + 96696546.

Almost surely, 2^105688728000 is an apocalyptic number.

105688728000 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 105688728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (202871710080).

105688728000 is an abundant number, since it is smaller than the sum of its proper divisors (300054692160).

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

105688728000 is a wasteful number, since it uses less digits than its factorization.

105688728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1222 (or 1199 counting only the distinct ones).

The product of its (nonzero) digits is 215040, while the sum is 45.

The spelling of 105688728000 in words is "one hundred five billion, six hundred eighty-eight million, seven hundred twenty-eight thousand".