1089

1089 is a natural number that lies between 1088 and 1090. In base-10 notation it is written as 1089, and it is the square of 33 (since 33 × 33 = 1089).

Mathematically, 1089 factors as 3^2 × 11^2, making it a perfect square. It can also be expressed as 9 × 121. Consequently, 1089 = 33^2, and its digits are the reverse of those in 9801, which equals 99^2.

The number is well known for the 1089 trick, a popular puzzle in recreational mathematics. Take any three-digit number abc with a ≠ c. Form N = 100a + 10b + c and its reverse R = 100c + 10b + a. Subtract the smaller from the larger to get D = |N − R|, which equals 99|a − c|. Treat D as a three-digit number (pad with a leading zero if needed), reverse its digits to get D_rev, and add: D + D_rev = 1089. For example, 732 − 237 = 495, and 495 + 594 = 1089.

In Roman numerals, 1089 is MLXXXIX. As a mathematical curiosity, it connects to the squares of 33 and 99 and to digit-reversal tricks used in recreational mathematics.