12321

12321 is a five-digit decimal number. It is a palindrome, reading the same forwards and backwards, and it is also a perfect square, equal to 111 squared.

The square root is 111. The prime factorization is 3^2 * 37^2, since 111 = 3 * 37. Therefore 12321 = (3 * 37)^2. The sum of its digits is 9, so it is divisible by 9. It is also a square of a repunit: 111 is the repunit with three ones, hence 12321 = (111)^2.

This number is part of a family of palindromic squares that arise from squaring repunits in base 10; for example, 1^2 = 1, 11^2 = 121, 111^2 = 12321, 1111^2 = 1234321, etc. The decimal representation forms a symmetric pattern 1-2-3-...-n-(...-3-2-1) with n = 3 here.

In mathematics and puzzles, 12321 is cited as a simple example of a palindromic square and of a square of a repunit. It illustrates how certain structured numbers produce mirrored digit patterns when squared.