Numberwise

1731

1731 is the year the first circulating library opened in Britain.

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Where 1731 fits

Where 1731 fits: Mathematics, History, Related numbersMathematics: Semiprime, Lucky number (mathematical sieve). History: Historical years. Related numbers: 1753.MathematicsSemiprimeLucky number (mathematical …HistoryHistorical yearsRelated numbers17531731
1731 connects to 3 worlds: mathematics, history, related numbers.

Why 1731 is special

Books were expensive enough that lending was a business. Subscription libraries spread reading well beyond those who could afford to buy.

Same number, different meanings

How 1731 is understood across different contexts — never implying one meaning because of another.

1731 is part of

Factors & digit properties

Divisors (4)
1, 3, 577, 1731
Prime factorisation
3 × 577
Digit sum
12
Digital root
3

Representations

Decimal
1731
Scientific notation
1.731 × 10^3

Roman numerals

M D C C X X X I

Binary

1 1 0 1 1 0 0 0 0 1 1

1 × 1,024 + 1 × 512 + 0 × 256 + 1 × 128 + 1 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 1,731

Octal

3 3 0 3

3 × 512 + 3 × 64 + 0 × 8 + 3 × 1 = 1,731

Hexadecimal

6 c 3

6 × 256 + c × 16 + 3 × 1 = 1,731

Read as powers of two: 1,024 + 512 + 128 + 64 + 2 + 1 = 1,731.

In historical numeral systems

Egyptian

1 lotus, 7 coils of rope, 3 hobbles, 1 stroke

1 × 1,000 + 7 × 100 + 3 × 10 + 1 × 1 = 1,731. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.

Babylonian

2 corner wedges + 8 vertical wedges (sixties place), 5 corner wedges + 1 vertical wedge (units place)

28 × 60 + 51 = 1731. 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

Related numbers & connections

Documented appearance
1731 is a year in the 18th century, in the 1730s.

1731 is a year in the 18th century, in the 1730s.

Connection
Circulating libraries from 1731 put reading within reach of people who could not buy books; the British Museum in 1753 was the first national museum free to the public.

Circulating libraries from 1731 put reading within reach of people who could not buy books; the British Museum in 1753 was the first national museum free to the public.

View 1753

Numbers Around Us

  • appears inHistorical years
    why?

    Strength 0.50, confidence "high".

Other connections

  • developed from1753
    why?

    Strength 0.50, confidence "high".

How is 1731 connected to another number? →

History

  • In 1731, the Library Company of Philadelphia was founded by Benjamin Franklin, an early subscription library (North America).

    DocumentedHistoryGeography: North AmericaPeriod: 1731

Culture

  • Circulating libraries from 1731 rented books by subscription, which put reading within reach of people who could not buy at all. Publishers initially treated them as a threat to sales.

    DocumentedCultureGeography: BritainPeriod: 1731

Common questions

Is 1731 a prime number?

No, 1731 is not prime.

What are the factors of 1731?

The factors of 1731 are 1, 3, 577, 1731.

What is 1731 in Roman numerals?

1731 in Roman numerals is MDCCXXXI.

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