• 289 is the smallest number with distinct digits such that divided by any of its digits leaves the same nonzero remainder. There are 40 such numbers, the largest being 843697.

• 289 can be written using four 4's:

289 has 3 divisors (see below), whose sum is σ = 307. Its totient is φ = 272.

The previous prime is 283. The next prime is 293. The reversal of 289 is 982.

289 = T_{16} + T_{17}.

The square root of 289 is 17.

It is a perfect power (a square), and thus also a powerful number.

289 is nontrivially palindromic in base 4 and base 16.

289 is an esthetic number in base 16, because in such base its adjacent digits differ by 1.

It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length, and also an emirpimes, since its reverse is a distinct semiprime: 982 = 2 ⋅491.

It can be written as a sum of positive squares in only one way, i.e., 225 + 64 = 15^2 + 8^2 .

It is not a de Polignac number, because 289 - 2^{3} = 281 is a prime.

It is a Duffinian number.

289 is an undulating number in base 16.

289 is a lucky number.

It is a plaindrome in base 10, base 14 and base 15.

It is a nialpdrome in base 8.

It is not an unprimeable number, because it can be changed into a prime (281) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 9 + ... + 25.

289 is a Friedman number, since it can be written as (9+8)^2, using all its digits and the basic arithmetic operations.

It is a Proth number, since it is equal to 9 ⋅ 2^{5} + 1 and 9 < 2^{5}.

289 is the 17-th square number.

289 is the 9-th centered octagonal number.

It is an amenable number.

289 is a deficient number, since it is larger than the sum of its proper divisors (18).

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

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

The sum of its prime factors is 34 (or 17 counting only the distinct ones).

The product of its digits is 144, while the sum is 19.

The cubic root of 289 is about 6.6114890185.

Multiplying 289 by its product of digits (144), we get a triangular number (41616 = T_{288}).

It can be divided in two parts, 28 and 9, that multiplied together give a palindrome (252).

The spelling of 289 in words is "two hundred eighty-nine", and thus it is an aban number.

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