105689735424000 has 6912 divisors, whose sum is σ = 519141968916480. Its totient is φ = 20437401600000.

The previous prime is 105689735423963. The next prime is 105689735424001. The reversal of 105689735424000 is 424537986501.

It is a happy number.

105689735424000 is a `hidden beast` number, since 1 + 0 + 5 + 6 + 8 + 97 + 3 + 542 + 4 + 0 + 0 + 0 = 666.

It is a super-5 number, since 5×105689735424000⁵ (a number of 71 digits) contains 55555 as substring. Note that it is a super-d number also for d = 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105689735424001) by changing a digit.

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 575 ways as a sum of consecutive naturals, for example, 1046433023950 + ... + 1046433024050.

It is an arithmetic number, because the mean of its divisors is an integer number (75107345040).

It is a 1-persistent number, because it is pandigital, but 2⋅105689735424000 = 211379470848000 is not.

Almost surely, 2^{105689735424000} is an apocalyptic number.

105689735424000 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 105689735424000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (259570984458240).

105689735424000 is an abundant number, since it is smaller than the sum of its proper divisors (413452233492480).

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

105689735424000 is a wasteful number, since it uses less digits than its factorization.

105689735424000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 225 (or 185 counting only the distinct ones).

The product of its (nonzero) digits is 7257600, while the sum is 54.

The spelling of 105689735424000 in words is "one hundred five trillion, six hundred eighty-nine billion, seven hundred thirty-five million, four hundred twenty-four thousand".