1654
1654 is the year probability theory was founded.
- Even
- Composite
Where 1654 fits
Why 1654 is special
Pascal and Fermat exchanged letters about how to divide the stakes in an interrupted game of chance. A gambling question produced the mathematics now underlying insurance, physics and statistics.
1654 is part of
Factors & digit properties
- Divisors (4)
- 1, 2, 827, 1654
- Prime factorisation
- 2 × 827
- Digit sum
- 16
- Digital root
- 7
Representations
- Decimal
- 1654
- Scientific notation
- 1.654 × 10^3
Roman numerals
M D C L I V
MDCLIV uses the subtractive pair IV: one before five — five minus one.
Binary
1 1 0 0 1 1 1 0 1 1 0
1 × 1,024 + 1 × 512 + 0 × 256 + 0 × 128 + 1 × 64 + 1 × 32 + 1 × 16 + 0 × 8 + 1 × 4 + 1 × 2 + 0 × 1 = 1,654
Octal
3 1 6 6
3 × 512 + 1 × 64 + 6 × 8 + 6 × 1 = 1,654
Hexadecimal
6 7 6
6 × 256 + 7 × 16 + 6 × 1 = 1,654
Read as powers of two: 1,024 + 512 + 64 + 32 + 16 + 4 + 2 = 1,654.
In historical numeral systems
Egyptian
1 lotus, 6 coils of rope, 5 hobbles, 4 strokes
1 × 1,000 + 6 × 100 + 5 × 10 + 4 × 1 = 1,654. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
2 corner wedges + 7 vertical wedges (sixties place), 3 corner wedges + 4 vertical wedges (units place)
27 × 60 + 34 = 1654. 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
- Semiprime
Related numbers & connections
1654 is a year in the 17th century, in the 1650s.
Euler's solution to the Königsberg bridges in 1736 created graph theory by discarding geography; the Pascal-Fermat letters of 1654 created probability from a gambling dispute. Both fields began from a puzzle.
View 1736 →Numbers Around Us
- appears inHistorical years
why?
Strength 0.50, confidence "high".
Other connections
- is associated with1736
why?
Strength 0.50, confidence "high".
Science
In 1654, correspondence between Pascal and Fermat on a gambling problem laid the foundations of probability theory (France).
DocumentedScienceGeography: FrancePeriod: 1654The Pascal-Fermat letters of 1654 addressed how to split a pot when a game is abandoned partway. Answering it required expected value, and probability theory follows from that exchange.
DocumentedScienceGeography: FrancePeriod: 1654
Common questions
Is 1654 a prime number?
No, 1654 is not prime.
What are the factors of 1654?
The factors of 1654 are 1, 2, 827, 1654.
What is 1654 in Roman numerals?
1654 in Roman numerals is MDCLIV. IV is subtractive: one before five — five minus one. Written additively it would be MDCLIIII, 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: 2 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026