105318688320 has 392 divisors, whose sum is σ = 398146594104. Its totient is φ = 26431930368.

The previous prime is 105318688309. The next prime is 105318688367. The reversal of 105318688320 is 23886813501.

105318688320 is a `hidden beast` number, since 1 + 0 + 5 + 318 + 6 + 8 + 8 + 320 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 19530621504 + 85788066816 = 139752^2 + 292896^2 .

It is a super-2 number, since 2×105318688320² (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 an unprimeable number.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 3952482 + ... + 3979038.

It is an arithmetic number, because the mean of its divisors is an integer number (1015680087).

Almost surely, 2^105318688320 is an apocalyptic number.

105318688320 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 105318688320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (199073297052).

105318688320 is an abundant number, since it is smaller than the sum of its proper divisors (292827905784).

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

105318688320 is an equidigital number, since it uses as much as digits as its factorization.

105318688320 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 26609 (or 26584 counting only the distinct ones).

The product of its (nonzero) digits is 276480, while the sum is 45.

The spelling of 105318688320 in words is "one hundred five billion, three hundred eighteen million, six hundred eighty-eight thousand, three hundred twenty".