189216 has 60 divisors (see below), whose sum is σ = 564102. Its totient is φ = 62208.

The previous prime is 189199. The next prime is 189223. The reversal of 189216 is 612981.

189216 = 3³ + 4³ + ... + 29³.

It can be written as a sum of positive squares in only one way, i.e., 156816 + 32400 = 396^2 + 180^2 .

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

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is an alternating number because its digits alternate between odd and even.

It is a self number, because there is not a number n which added to its sum of digits gives 189216.

It is an unprimeable number.

189216 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 9 ways as a sum of consecutive naturals, for example, 2556 + ... + 2628.

2¹⁸⁹²¹⁶ is an apocalyptic number.

189216 is a gapful number since it is divisible by the number (16) 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 189216, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (282051).

189216 is an abundant number, since it is smaller than the sum of its proper divisors (374886).

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

189216 is an equidigital number, since it uses as much as digits as its factorization.

189216 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 95 (or 78 counting only the distinct ones).

The product of its digits is 864, while the sum is 27.

The square root of 189216 is about 434.9896550494. The cubic root of 189216 is about 57.4097892307.

It can be divided in two parts, 18921 and 6, that multiplied together give a triangular number (113526 = T₄₇₆).

The spelling of 189216 in words is "one hundred eighty-nine thousand, two hundred sixteen".