105312 has 24 divisors (see below), whose sum is σ = 276696. Its totient is φ = 35072.

The previous prime is 105277. The next prime is 105319. The reversal of 105312 is 213501.

It is a tau number, because it is divible by the number of its divisors (24).

It is a super-2 number, since 2×105312² = 22181234688, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a zygodrome in base 5.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105319) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 453 + ... + 644.

It is an arithmetic number, because the mean of its divisors is an integer number (11529).

2¹⁰⁵³¹² is an apocalyptic number.

105312 is a gapful number since it is divisible by the number (12) formed by its first and last digit.

It is an amenable number.

105312 is an abundant number, since it is smaller than the sum of its proper divisors (171384).

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

105312 is a wasteful number, since it uses less digits than its factorization.

105312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1110 (or 1102 counting only the distinct ones).

The product of its (nonzero) digits is 30, while the sum is 12.

The square root of 105312 is about 324.5181042715. The cubic root of 105312 is about 47.2236212324.

Adding to 105312 its reverse (213501), we get a palindrome (318813).

The spelling of 105312 in words is "one hundred five thousand, three hundred twelve".