1,089
1,089 is the result of a digit-reversal trick that works on almost every three-digit number.
Where 1,089 fits
Why 1,089 is special
Take any three-digit number whose first and last digits differ by at least two, reverse it, subtract the smaller from the larger, then add that result to its own reverse. The answer is 1,089 every time. The trick is a staple of recreational mathematics because the algebra behind it is simple enough to show a child yet the result feels like sleight of hand.
1,089 connects to:
- historical years — appears in
- 196 — contrasts with
Same number, different meanings
How 1,089 is understood across different contexts — never implying one meaning because of another.
- Mathematics
Take any three-digit number whose first and last digits differ by at least two, reverse it, subtract the smaller from the larger, then add that result to its own reverse. The answer is 1,089 every time. The trick is a staple of recreational mathematics because the algebra behind it is simple enough to show a child yet the result feels like sleight of hand.
- History
In 1089, an earthquake was recorded across England, unusual enough that chroniclers noted it in several places (England).
- Media & popular culture
Because the routine always produces 1089, it is used as a prediction effect: a performer seals the answer in an envelope before the volunteer chooses a number. The mathematics is doing all the work and the presentation is doing none, which is why it appears in books of mathematical recreations rather than in conjuring manuals — the standard reference is David Acheson's book named for the number.
1,089 is part of
Factors & digit properties
- Divisors (9)
- 1, 3, 9, 11, 33, 99, 121, 363, 1089
- Prime factorisation
- 3^2 × 11^2
- Digit sum
- 18
- Digital root
- 9
Representations
- Decimal
- 1089
- Scientific notation
- 1.089 × 10^3
Roman numerals
M L X X X I X
MLXXXIX uses the subtractive pair IX: one before ten — ten minus one.
Binary
1 0 0 0 1 0 0 0 0 0 1
1 × 1,024 + 0 × 512 + 0 × 256 + 0 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 1,089
Octal
2 1 0 1
2 × 512 + 1 × 64 + 0 × 8 + 1 × 1 = 1,089
Hexadecimal
4 4 1
4 × 256 + 4 × 16 + 1 × 1 = 1,089
Read as powers of two: 1,024 + 64 + 1 = 1,089.
In historical numeral systems
Egyptian
1 lotus, 8 hobbles, 9 strokes
1 × 1,000 + 8 × 10 + 9 × 1 = 1,089. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
1 corner wedge + 8 vertical wedges (sixties place), 9 vertical wedges (units place)
18 × 60 + 9 = 1089. Places are separated by a space on the tablet, with the higher place written first.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Deficient number
- Powerful number
Related numbers & connections
1089 is a year in the 11th century, in the 1080s.
Both are digit-reversal curiosities. 1089 always works and is a parlour trick; 196 has resisted a billion digits of computation and is an open problem.
View 196 →Numbers Around Us
- appears inHistorical years
why?
Strength 0.50, confidence "high".
Other connections
- contrasts with196
why?
Strength 0.50, confidence "high".
History
In 1089, an earthquake was recorded across England, unusual enough that chroniclers noted it in several places (England).
DocumentedHistoryGeography: EnglandPeriod: 1089
Media & popular culture
Because the routine always produces 1089, it is used as a prediction effect: a performer seals the answer in an envelope before the volunteer chooses a number. The mathematics is doing all the work and the presentation is doing none, which is why it appears in books of mathematical recreations rather than in conjuring manuals — the standard reference is David Acheson's book named for the number.
DocumentedMedia & popular culture
Mathematics
Write the three-digit number as 100a + 10b + c. Subtracting its reverse gives 99(a − c), which for any difference of at least two is one of 198, 297, 396, 495, 594, 693, 792 or 891 — and every one of those, added to its own reverse, is 1,089. The trick is exhaustive rather than mysterious.
DocumentedMathematics1089 = 33², and multiplying it by 9 gives 9801, which is 1089 written backwards — and 99². The pattern continues: 10989 × 9 = 98901, and so on with nines inserted in the middle. These are consequences of how multiplying by 9 interacts with base-10 place value, which is the same reason the reverse-and-subtract trick lands on 1089 in the first place.
DocumentedMathematics
Common questions
What is the 1089 trick?
Take a three-digit number whose first and last digits differ by at least two, reverse it, subtract the smaller from the larger, then add that answer to its own reverse. The result is 1,089 every time. The reason is exhaustive rather than mysterious: the subtraction always gives 99 × (first digit − last), which is one of only eight values, and each of those plus its reverse is 1,089.
Is 1,089 a prime number?
No, 1,089 is not prime.
What are the factors of 1,089?
The factors of 1,089 are 1, 3, 9, 11, 33, 99, 121, 363, 1089.
What is 1,089 in Roman numerals?
1,089 in Roman numerals is MLXXXIX. IX is subtractive: one before ten — ten minus one. Written additively it would be MLXXXVIIII, which Roman inscriptions used freely — the strict subtractive form is a later convention.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 4 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026