72189 has 12 divisors (see below), whose sum is σ = 112476. Its totient is φ = 44352.

The previous prime is 72173. The next prime is 72211. The reversal of 72189 is 98127.

It can be written as a sum of positive squares in 2 ways, for example, as 5625 + 66564 = 75^2 + 258^2 .

It is not a de Polignac number, because 72189 - 2⁴ = 72173 is a prime.

It is a super-2 number, since 2×72189² = 10422503442, which contains 22 as substring.

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

It is a Curzon number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72109) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 192 + ... + 425.

It is an arithmetic number, because the mean of its divisors is an integer number (9373).

2⁷²¹⁸⁹ is an apocalyptic number.

It is an amenable number.

72189 is a deficient number, since it is larger than the sum of its proper divisors (40287).

72189 is a wasteful number, since it uses less digits than its factorization.

72189 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 636 (or 633 counting only the distinct ones).

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

The square root of 72189 is about 268.6801071907. The cubic root of 72189 is about 41.6380461230.

It can be divided in two parts, 7218 and 9, that added together give a palindrome (7227).

The spelling of 72189 in words is "seventy-two thousand, one hundred eighty-nine".