Overview

1738 refers both to a specific year in the 18th century and to the integer 1738. As a year it falls within the period commonly called the Enlightenment, when intellectual exchange, diplomatic realignments and imperial competition shaped Europe and overseas territories. As a number it is an ordinary even composite integer with elementary arithmetic features used in reference works and recreational mathematics.

Mathematical properties

The integer 1738 factors as 2 × 11 × 79. Its positive divisors are 1, 2, 11, 22, 79, 158, 869 and 1738. The sum of the proper divisors equals 1,142, which is less than 1,738, so the number is classified as deficient. The sum of all divisors (the sigma function) is 2,880. Its Euler totient (φ) is 780. In Roman numerals it is written MDCCXXXVIII; in hexadecimal it is 6CA and its binary representation is 11011001010. These attributes place 1738 among well-behaved composite numbers with three prime factors.

Notable events of the year 1738

  • Diplomacy: European powers continued to settle scores from earlier conflicts, and treaties and negotiations in this period adjusted borders and dynastic claims, notably affecting Italian and central European territories.
  • Religion and society: In England a widely reported spiritual turning point for the preacher John Wesley became central to the Methodist movement and to later accounts of evangelical revival.
  • Culture and the arts: Courtly patronage and public institutions supported opera, theater and the visual arts; composers, performers and impresarios were active in major cultural centres.

Cultural and historical context

The decade around 1738 saw the spread of Enlightenment ideas through books, salons and learned societies, alongside improvements in navigation, natural history and classification that aided exploration and commerce. Colonial expansion and rivalry persisted outside Europe, while scientific correspondence and print culture increased the circulation of new knowledge. Social life continued to be shaped by local politics, economic change and networks of patronage.

Legacy and uses

Historically, 1738 is remembered for developments in church history and for diplomatic settlements that contributed to the map of 18th-century Europe. Numerically, 1738 appears as an identifier in registers, catalogues and examples in arithmetic and number theory. Its simple factorization and explicit divisor structure make it straightforward to illustrate basic multiplicative functions and elementary properties of integers.

Further notes

When treating 1738 either as a year or a number, sources typically distinguish between widely accepted facts—such as the occurrence of Wesley's Aldersgate experience in 1738 and the number's prime factorization—and more detailed claims (precise treaty clauses, exact dates, or minor local events) that require specific citation. For general overviews, 1738 serves as a representative year of mid-18th-century developments and as a modestly interesting composite integer.