1089 (number)

1089 (number)

1089 is the integer after 1088 and before 1090. It is a square number (33 squared), a nonagonal number, a 32-gonal number, a 364-gonal number, and a centered octagonal number.

In base 10, the following steps always yield 1089:

1. Take any three-digit number where the first and last digits differ by 2 or more.
2. Reverse the digits, and subtract the smaller from the larger one.
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. Also note the patterns within each column.

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.

1089 is the first reverse-divisible number. The next is 2178 (= 1089 * 2 = 8712/4), and they are the only four-digit numbers that are reverse divisible.