105204386304 has 600 divisors, whose sum is σ = 344842108380. Its totient is φ = 31818645504.

The previous prime is 105204386299. The next prime is 105204386323. The reversal of 105204386304 is 403683402501.

105204386304 is a `hidden beast` number, since 10 + 5 + 2 + 0 + 4 + 3 + 8 + 630 + 4 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 104509958400 + 694427904 = 323280^2 + 26352^2 .

It is a super-3 number, since 3×105204386304³ (a number of 34 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 965177802 + ... + 965177910.

Almost surely, 2^105204386304 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105204386304, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (172421054190).

105204386304 is an abundant number, since it is smaller than the sum of its proper divisors (239637722076).

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

105204386304 is an equidigital number, since it uses as much as digits as its factorization.

105204386304 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 230 (or 168 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 36.

Adding to 105204386304 its reverse (403683402501), we get a palindrome (508887788805).

The spelling of 105204386304 in words is "one hundred five billion, two hundred four million, three hundred eighty-six thousand, three hundred four".