105393312 has 120 divisors (see below), whose sum is σ = 314768916. Its totient is φ = 34587648.

The previous prime is 105393289. The next prime is 105393331. The reversal of 105393312 is 213393501.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 100881936 + 4511376 = 10044^2 + 2124^2 .

It is a super-2 number, since 2×105393312² = 22215500428658688, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 188938 + ... + 189494.

Almost surely, 2^105393312 is an apocalyptic number.

105393312 is a gapful number since it is divisible by the number (12) 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 105393312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (157384458).

105393312 is an abundant number, since it is smaller than the sum of its proper divisors (209375604).

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

105393312 is an equidigital number, since it uses as much as digits as its factorization.

105393312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 652 (or 635 counting only the distinct ones).

The product of its (nonzero) digits is 2430, while the sum is 27.

The square root of 105393312 is about 10266.1244878484. The cubic root of 105393312 is about 472.3577198212.

The spelling of 105393312 in words is "one hundred five million, three hundred ninety-three thousand, three hundred twelve".