189072 has 60 divisors (see below), whose sum is σ = 575484. Its totient is φ = 57600.

The previous prime is 189067. The next prime is 189127. The reversal of 189072 is 270981.

It can be written as a sum of positive squares in 2 ways, for example, as 112896 + 76176 = 336^2 + 276^2 .

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

It is an unprimeable 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 11 ways as a sum of consecutive naturals, for example, 1822 + ... + 1922.

2¹⁸⁹⁰⁷² is an apocalyptic number.

189072 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 189072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (287742).

189072 is an abundant number, since it is smaller than the sum of its proper divisors (386412).

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

189072 is a wasteful number, since it uses less digits than its factorization.

189072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 128 (or 119 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 27.

The square root of 189072 is about 434.8241023678. The cubic root of 189072 is about 57.3952219149.

The spelling of 189072 in words is "one hundred eighty-nine thousand, seventy-two".