1645
1645 is the year of the Battle of Naseby.
- Odd
- Composite
Where 1645 fits
Why 1645 is special
The New Model Army destroyed the royalist field army and captured the king's correspondence, which was published and showed him negotiating for foreign Catholic troops.
1645 is part of
Factors & digit properties
- Divisors (8)
- 1, 5, 7, 35, 47, 235, 329, 1645
- Prime factorisation
- 5 × 7 × 47
- Digit sum
- 16
- Digital root
- 7
Representations
- Decimal
- 1645
- Scientific notation
- 1.645 × 10^3
Roman numerals
M D C X L V
MDCXLV uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 1 0 0 1 1 0 1 1 0 1
1 × 1,024 + 1 × 512 + 0 × 256 + 0 × 128 + 1 × 64 + 1 × 32 + 0 × 16 + 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 1,645
Octal
3 1 5 5
3 × 512 + 1 × 64 + 5 × 8 + 5 × 1 = 1,645
Hexadecimal
6 6 d
6 × 256 + 6 × 16 + d × 1 = 1,645
Read as powers of two: 1,024 + 512 + 64 + 32 + 8 + 4 + 1 = 1,645.
In historical numeral systems
Egyptian
1 lotus, 6 coils of rope, 4 hobbles, 5 strokes
1 × 1,000 + 6 × 100 + 4 × 10 + 5 × 1 = 1,645. 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), 2 corner wedges + 5 vertical wedges (units place)
27 × 60 + 25 = 1645. 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
- Lucky number (mathematical sieve)
Related numbers & connections
1645 is a year in the 17th century, in the 1640s.
Naseby in 1645 destroyed the royalist army and captured the king's correspondence; Charles I was executed four years later.
View 1649 →Numbers Around Us
- appears inHistorical years
why?
Strength 0.50, confidence "high".
Other connections
- developed from1649
why?
Strength 0.50, confidence "high".
History
In 1645, the New Model Army decisively defeated the royalists at Naseby, effectively deciding the first English Civil War (England).
DocumentedHistoryGeography: EnglandPeriod: 1645Naseby in 1645 destroyed the royalist army and captured Charles I's private papers. Publishing them, showing him seeking Irish and continental Catholic help, did lasting damage to his cause.
DocumentedHistoryGeography: EnglandPeriod: 1645
Common questions
Is 1645 a prime number?
No, 1645 is not prime.
What are the factors of 1645?
The factors of 1645 are 1, 5, 7, 35, 47, 235, 329, 1645.
What is 1645 in Roman numerals?
1645 in Roman numerals is MDCXLV. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be MDCXXXXV, 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