1328 (number and year)

Numeric characteristics and representations

As an integer, 1328 is an even composite number. Its prime factorization is 2^4 × 83, so it equals 16 × 83. The positive divisors are 1, 2, 4, 8, 16, 83, 166, 332, 664 and 1328, giving ten divisors in total. The sum of all divisors is 2604, and the sum of proper divisors (1276) is less than the number itself, which classifies 1328 as a deficient number. Its Euler totient value is 656.

Common positional representations include binary 10100110000, hexadecimal 0x530, and Roman numerals MCCCXXVIII. In binary it contains four 1-bits, so it is an example of an "evil" number in the binary-parity classification (numbers with an even number of ones in their binary expansion).

Notable events in the year 1328 (CE)

The year 1328 in the Late Middle Ages saw a number of diplomatic and military developments in Western Europe. One important diplomatic settlement that year formally recognized the independence of Scotland after prolonged conflict with England. In France, the death of the last direct Capetian king produced a succession crisis that resulted in the accession of Philip of Valois as King Philip VI and the establishment of the Valois dynasty; that succession dispute was one of several factors contributing to tensions between France and England in the following decades. Military action in 1328 included the suppression of an uprising in Flanders by French royal forces.

Contexts, uses and distinctions

• Mathematics: 1328 appears in examples illustrating factorization, divisor functions, totient values and base conversions in elementary number theory and computing.
• Chronology: As a year, 1328 is referenced in medieval political, diplomatic and military history; it lies in the period of the Avignon Papacy and the tensions that preluded later Anglo-French wars.
• Identifiers: Like any four-digit integer, 1328 is used widely as a label in catalogues, models, addresses and archival references without intrinsic special meaning.

In both senses—numeric and calendrical—1328 is largely unexceptional as an integer but historically consequential as a year because of dynastic and diplomatic developments that influenced later European history.