1513
1513 is the year Machiavelli wrote The Prince.
- Odd
- Composite
Where 1513 fits
Why 1513 is special
It was written to seek employment from the Medici who had just removed him from office. Whether it is sincere advice or satire has been argued since publication, and the ambiguity is part of why it endures.
Same number, different meanings
How 1513 is understood across different contexts — never implying one meaning because of another.
- Mathematics
It was written to seek employment from the Medici who had just removed him from office. Whether it is sincere advice or satire has been argued since publication, and the ambiguity is part of why it endures.
- History
In 1513, Machiavelli wrote The Prince while excluded from Florentine politics (Italy).
- Culture
The Prince was written by an unemployed official hoping to impress the rulers who had dismissed and tortured him. Reading it as genuine counsel or as satire produces entirely different books, and the question is unresolved.
1513 is part of
Factors & digit properties
- Divisors (4)
- 1, 17, 89, 1513
- Prime factorisation
- 17 × 89
- Digit sum
- 10
- Digital root
- 1
Representations
- Decimal
- 1513
- Scientific notation
- 1.513 × 10^3
Roman numerals
M D X I I I
Binary
1 0 1 1 1 1 0 1 0 0 1
1 × 1,024 + 0 × 512 + 1 × 256 + 1 × 128 + 1 × 64 + 1 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 1,513
Octal
2 7 5 1
2 × 512 + 7 × 64 + 5 × 8 + 1 × 1 = 1,513
Hexadecimal
5 e 9
5 × 256 + e × 16 + 9 × 1 = 1,513
Read as powers of two: 1,024 + 256 + 128 + 64 + 32 + 8 + 1 = 1,513.
In historical numeral systems
Egyptian
1 lotus, 5 coils of rope, 1 hobble, 3 strokes
1 × 1,000 + 5 × 100 + 1 × 10 + 3 × 1 = 1,513. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
2 corner wedges + 5 vertical wedges (sixties place), 1 corner wedge + 3 vertical wedges (units place)
25 × 60 + 13 = 1513. 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
1513 is a year in the 16th century, in the 1510s.
Numbers Around Us
- appears inHistorical years
why?
Strength 0.50, confidence "high".
History
In 1513, Machiavelli wrote The Prince while excluded from Florentine politics (Italy).
DocumentedHistoryGeography: ItalyPeriod: 1513In 1513, Balboa crossed the isthmus of Panama and sighted the Pacific (Central America).
DocumentedHistoryGeography: Central AmericaPeriod: 1513In 1513, the Scottish king and much of his nobility were killed at Flodden (Scotland).
DocumentedHistoryGeography: ScotlandPeriod: 1513
Culture
The Prince was written by an unemployed official hoping to impress the rulers who had dismissed and tortured him. Reading it as genuine counsel or as satire produces entirely different books, and the question is unresolved.
DocumentedCultureGeography: FlorencePeriod: 1513
Common questions
Is 1513 a prime number?
No, 1513 is not prime.
What are the factors of 1513?
The factors of 1513 are 1, 17, 89, 1513.
What is 1513 in Roman numerals?
1513 in Roman numerals is MDXIII.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 4 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026