1640
1640 is the year Portugal regained independence from Spain.
- Even
- Composite
Where 1640 fits
Why 1640 is special
Sixty years of Spanish rule ended in a coup, and the war of restoration ran a further 28 years before Spain recognised it.
1640 is part of
Factors & digit properties
- Divisors (16)
- 1, 2, 4, 5, 8, 10, 20, 40, 41, 82, 164, 205, 328, 410, 820, 1640
- Prime factorisation
- 2^3 × 5 × 41
- Digit sum
- 11
- Digital root
- 2
Representations
- Decimal
- 1640
- Scientific notation
- 1.640 × 10^3
Roman numerals
M D C X L
MDCXL uses the subtractive pair XL: ten before fifty — fifty minus ten.
Binary
1 1 0 0 1 1 0 1 0 0 0
1 × 1,024 + 1 × 512 + 0 × 256 + 0 × 128 + 1 × 64 + 1 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 1,640
Octal
3 1 5 0
3 × 512 + 1 × 64 + 5 × 8 + 0 × 1 = 1,640
Hexadecimal
6 6 8
6 × 256 + 6 × 16 + 8 × 1 = 1,640
Read as powers of two: 1,024 + 512 + 64 + 32 + 8 = 1,640.
In historical numeral systems
Egyptian
1 lotus, 6 coils of rope, 4 hobbles
1 × 1,000 + 6 × 100 + 4 × 10 = 1,640. 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 (units place)
27 × 60 + 20 = 1640. 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
- Abundant number
Related numbers & connections
1640 is a year in the 17th century, in the 1640s.
Portugal declared independence from Spain in 1640 and Spain recognised it in 1668 — a coup that took a day and a war that took twenty-eight years.
View 1668 →Numbers Around Us
- appears inHistorical years
why?
Strength 0.50, confidence "high".
Other connections
- developed from1668
why?
Strength 0.50, confidence "high".
History
In 1640, the Long Parliament assembled, sitting in some form for two decades and reshaping the constitutional balance (England).
DocumentedHistoryGeography: EnglandPeriod: 1640Portugal's 1640 restoration took a day to declare and 28 years to secure. Spain did not recognise Portuguese independence until 1668.
DocumentedHistoryGeography: Portugal and SpainPeriod: 1640–1668
Common questions
Is 1640 a prime number?
No, 1640 is not prime.
What are the factors of 1640?
The factors of 1640 are 1, 2, 4, 5, 8, 10, 20, 40, 41, 82, 164, 205, 328, 410, 820, 1640.
What is 1640 in Roman numerals?
1640 in Roman numerals is MDCXL. XL is subtractive: ten before fifty — fifty minus ten. Written additively it would be MDCXXXX, 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