843
843 is the year the Treaty of Verdun divided the Carolingian Empire.
- Odd
- Composite
Where 843 fits
Why 843 is special
Charlemagne's empire was split three ways among his grandsons, and the boundaries drawn roughly prefigure France, Germany and a contested strip between them fought over for the next eleven centuries.
Factors & digit properties
- Divisors (4)
- 1, 3, 281, 843
- Prime factorisation
- 3 × 281
- Digit sum
- 15
- Digital root
- 6
Representations
- Decimal
- 843
- Scientific notation
- 8.430 × 10^2
Roman numerals
D C C C X L I I I
DCCCXLIII uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 1 0 1 0 0 1 0 1 1
1 × 512 + 1 × 256 + 0 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 843
Octal
1 5 1 3
1 × 512 + 5 × 64 + 1 × 8 + 3 × 1 = 843
Hexadecimal
3 4 b
3 × 256 + 4 × 16 + b × 1 = 843
Read as powers of two: 512 + 256 + 64 + 8 + 2 + 1 = 843.
In historical numeral systems
Egyptian
8 coils of rope, 4 hobbles, 3 strokes
8 × 100 + 4 × 10 + 3 × 1 = 843. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
1 corner wedge + 4 vertical wedges (sixties place), 3 vertical wedges (units place)
14 × 60 + 3 = 843. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
omega, then mu, then gamma, marked as a numeral
omega-mu-gamma + keraia
omega + mu + gamma written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
tav, then tav, then mem, then gimel
tav-tav-mem-gimel
tav (400) + tav (400) + mem (40) + gimel (3) = 843, written in descending order.
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
- Semiprime
- Lucas number
Related numbers & connections
Charlemagne was crowned in 800 and his empire was divided at Verdun in 843, drawing a border between France and Germany that was contested into the twentieth century.
View 800 →Other connections
- developed from800
why?
Strength 0.50, confidence "high".
History
Verdun in 843 divided the Frankish empire into western, eastern and middle kingdoms. The middle strip — Lotharingia — became the contested ground between France and Germany into the twentieth century.
DocumentedHistoryGeography: Carolingian EmpirePeriod: 843
Common questions
Is 843 a prime number?
No, 843 is not prime.
What are the factors of 843?
The factors of 843 are 1, 3, 281, 843.
What is 843 in Roman numerals?
843 in Roman numerals is DCCCXLIII. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be DCCCXXXXIII, 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: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026