1089 (number) - Definition and Overview

1089 is the number after 1088 and before 1090. It is 33 squared, a nonagonal number and a centered octagonal number.

It has some interesting mathematical properties.

The number 1089 is the result of the following experiment:

1. Take any three-digit integer in which the first digit is at least two more than the last.
2. Reverse the digits, and subtract the result from the original number.
3. Add to this result the number produced by reversing its digits.

For example:

732 - 237 = 495
495 + 594 = 1089

Multiplying the number 1089 by the integers from 1 to 9 produces a pattern: multipliers adding up to 10 give products that are the digit reversals of each other.

1 x 1089 = 1089
2 x 1089 = 2178
3 x 1089 = 3267
4 x 1089 = 4356
5 x 1089 = 5445
6 x 1089 = 6534
7 x 1089 = 7623
8 x 1089 = 8712
9 x 1089 = 9801

Numbers formed analogously in other bases, e.g. octal 1067 or hexadecimal 10EF, also have these properties.