105838363800 has 768 divisors, whose sum is σ = 419306496000. Its totient is φ = 24320839680.

The previous prime is 105838363699. The next prime is 105838363801. The reversal of 105838363800 is 8363838501.

105838363800 is a `hidden beast` number, since 1 + 0 + 5 + 8 + 3 + 8 + 3 + 638 + 0 + 0 = 666.

It is a super-2 number, since 2×105838363800² (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 not an unprimeable number, because it can be changed into a prime (105838363801) by changing a digit.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 97366857 + ... + 97367943.

It is an arithmetic number, because the mean of its divisors is an integer number (545972000).

Almost surely, 2^105838363800 is an apocalyptic number.

105838363800 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 105838363800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (209653248000).

105838363800 is an abundant number, since it is smaller than the sum of its proper divisors (313468132200).

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

105838363800 is a wasteful number, since it uses less digits than its factorization.

105838363800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1217 (or 1202 counting only the distinct ones).

The product of its (nonzero) digits is 414720, while the sum is 45.

The spelling of 105838363800 in words is "one hundred five billion, eight hundred thirty-eight million, three hundred sixty-three thousand, eight hundred".