189312 has 64 divisors (see below), whose sum is σ = 550800. Its totient is φ = 57344.

The previous prime is 189311. The next prime is 189337. The reversal of 189312 is 213981.

189312 is nontrivially palindromic in base 14.

It is a tau number, because it is divible by the number of its divisors (64).

It is a hoax number, since the sum of its digits (24) 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 (24).

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 189312.

It is not an unprimeable number, because it can be changed into a prime (189311) by changing a digit.

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, 6514 + ... + 6542.

2¹⁸⁹³¹² is an apocalyptic number.

189312 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 189312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (275400).

189312 is an abundant number, since it is smaller than the sum of its proper divisors (361488).

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

189312 is a wasteful number, since it uses less digits than its factorization.

189312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 63 (or 51 counting only the distinct ones).

The product of its digits is 432, while the sum is 24.

The square root of 189312 is about 435.0999885084. The cubic root of 189312 is about 57.4194966690.

The spelling of 189312 in words is "one hundred eighty-nine thousand, three hundred twelve".