105285312 has 224 divisors, whose sum is σ = 351129600. Its totient is φ = 30643200.

The previous prime is 105285307. The next prime is 105285319. The reversal of 105285312 is 213582501.

It is a happy number.

105285312 is a `hidden beast` number, since 105 + 28 + 531 + 2 = 666.

It is a super-2 number, since 2×105285312² = 22169993845874688, which contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (105285319) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 551137 + ... + 551327.

Almost surely, 2^105285312 is an apocalyptic number.

105285312 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 105285312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (175564800).

105285312 is an abundant number, since it is smaller than the sum of its proper divisors (245844288).

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

105285312 is a wasteful number, since it uses less digits than its factorization.

105285312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 252 (or 236 counting only the distinct ones).

The product of its (nonzero) digits is 2400, while the sum is 27.

The square root of 105285312 is about 10260.8631215897. The cubic root of 105285312 is about 472.1963178367.

The spelling of 105285312 in words is "one hundred five million, two hundred eighty-five thousand, three hundred twelve".