1782
1782 is the year the bald eagle was adopted as the US national emblem.
- Even
- Composite
Where 1782 fits
Why 1782 is special
Franklin's often-quoted objection, calling it a bird of bad moral character, comes from a private letter and was not an argument for the turkey as commonly retold.
Same number, different meanings
How 1782 is understood across different contexts — never implying one meaning because of another.
- Mathematics
Franklin's often-quoted objection, calling it a bird of bad moral character, comes from a private letter and was not an argument for the turkey as commonly retold.
- Technology & computing
In 1782, James Watt patented the double-acting rotative steam engine, making steam power usable for machinery rather than only pumping (Great Britain).
- Culture
Franklin did criticise the bald eagle's character in a 1784 letter to his daughter. He did not propose the turkey as the national bird, which is a later embellishment repeated as fact.
1782 is part of
Factors & digit properties
- Divisors (20)
- 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 81, 99, 162, 198, 297, 594, 891, 1782
- Prime factorisation
- 2 × 3^4 × 11
- Digit sum
- 18
- Digital root
- 9
Representations
- Decimal
- 1782
- Scientific notation
- 1.782 × 10^3
Roman numerals
M D C C L X X X I I
Binary
1 1 0 1 1 1 1 0 1 1 0
1 × 1,024 + 1 × 512 + 0 × 256 + 1 × 128 + 1 × 64 + 1 × 32 + 1 × 16 + 0 × 8 + 1 × 4 + 1 × 2 + 0 × 1 = 1,782
Octal
3 3 6 6
3 × 512 + 3 × 64 + 6 × 8 + 6 × 1 = 1,782
Hexadecimal
6 f 6
6 × 256 + f × 16 + 6 × 1 = 1,782
Read as powers of two: 1,024 + 512 + 128 + 64 + 32 + 16 + 4 + 2 = 1,782.
In historical numeral systems
Egyptian
1 lotus, 7 coils of rope, 8 hobbles, 2 strokes
1 × 1,000 + 7 × 100 + 8 × 10 + 2 × 1 = 1,782. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
2 corner wedges + 9 vertical wedges (sixties place), 4 corner wedges + 2 vertical wedges (units place)
29 × 60 + 42 = 1782. 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
- Harshad (Niven) number
Related numbers & connections
1782 is a year in the 18th century, in the 1780s.
Numbers Around Us
- appears inHistorical years
why?
Strength 0.50, confidence "high".
Technology & computing
In 1782, James Watt patented the double-acting rotative steam engine, making steam power usable for machinery rather than only pumping (Great Britain).
DocumentedTechnology & computingGeography: Great BritainPeriod: 1782
Culture
Franklin did criticise the bald eagle's character in a 1784 letter to his daughter. He did not propose the turkey as the national bird, which is a later embellishment repeated as fact.
DocumentedCultureGeography: United StatesPeriod: 1782
Common questions
Is 1782 a prime number?
No, 1782 is not prime.
What are the factors of 1782?
The factors of 1782 are 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 81, 99, 162, 198, 297, 594, 891, 1782.
What is 1782 in Roman numerals?
1782 in Roman numerals is MDCCLXXXII.
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