105310319400 has 672 divisors, whose sum is σ = 431365828320. Its totient is φ = 23561280000.

The previous prime is 105310319399. The next prime is 105310319417. The reversal of 105310319400 is 4913013501.

105310319400 is a `hidden beast` number, since 10 + 531 + 0 + 31 + 94 + 0 + 0 = 666.

It is a super-2 number, since 2×105310319400² (a number of 23 digits) contains 22 as substring.

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

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 167 ways as a sum of consecutive naturals, for example, 20846875 + ... + 20851925.

It is an arithmetic number, because the mean of its divisors is an integer number (641913435).

Almost surely, 2^105310319400 is an apocalyptic number.

105310319400 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 105310319400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (215682914160).

105310319400 is an abundant number, since it is smaller than the sum of its proper divisors (326055508920).

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

105310319400 is a wasteful number, since it uses less digits than its factorization.

105310319400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5109 (or 5085 counting only the distinct ones).

The product of its (nonzero) digits is 1620, while the sum is 27.

The spelling of 105310319400 in words is "one hundred five billion, three hundred ten million, three hundred nineteen thousand, four hundred".