305688 has 32 divisors (see below), whose sum is σ = 783360. Its totient is φ = 99360.

The previous prime is 305663. The next prime is 305717. The reversal of 305688 is 886503.

It is a Smith number, since the sum of its digits (30) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 305688.

It is an unprimeable number.

305688 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 993 + ... + 1263.

It is an arithmetic number, because the mean of its divisors is an integer number (24480).

2³⁰⁵⁶⁸⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 305688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (391680).

305688 is an abundant number, since it is smaller than the sum of its proper divisors (477672).

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

305688 is a wasteful number, since it uses less digits than its factorization.

305688 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 327 (or 323 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 30.

The square root of 305688 is about 552.8905859209. The cubic root of 305688 is about 67.3637305705.

The spelling of 305688 in words is "three hundred five thousand, six hundred eighty-eight".