1089 (number)

1089 (number)

1089 is the integer after 1088 and before 1090.

1089
Cardinal One thousand and eighty-nine
Ordinal 1089th
Factorization 1089 = 3^2 \cdot 11^2
Binary 10001000001
Hexadecimal 441

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

Other uses

References

  1. ^ Microsoft, Microsoft Office Word 2007 Rich Text Format (RTF) Specification February (2007): 142. The hexadecimal number 441 (decimal 1089) is identified with "Kiswahili (Kenya)."

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