Overview

1332 may refer to the integer following 1331 and preceding 1333, or to the calendar year AD 1332 in the 14th century. As a number it appears in counting, indexing and numbering systems; as a year it sits in the Late Middle Ages, a period of dynastic competition and social change in Europe and beyond.

Mathematical properties

Arithmetically, 1332 = 2^2 × 3^2 × 37. It is even, composite and not squarefree (it contains squared prime factors). The number of positive divisors is 18; the complete list is 1, 2, 3, 4, 6, 9, 12, 18, 36, 37, 74, 111, 148, 222, 333, 444, 666 and 1332. The sum of all divisors (sigma) is 3,458, so the sum of proper divisors is 2,126, which makes 1332 an abundant number. Its Euler totient is φ(1332) = 432. In base ten the digits add to 9, so 1332 is divisible by 9 and is a Harshad number. It is also a refactorable number because its divisor count 18 divides 1332 evenly. Representations in common bases include binary 10100110100, octal 2464 and hexadecimal 0x534. In Roman numerals it is MCCCXXXII.

Year AD 1332: historical context

The year 1332 falls within a turbulent phase of medieval history. In Scotland and neighboring regions the early 1330s involved conflicts over succession and independence, including actions associated with the Second War of Scottish Independence. Across western Europe noble rivalries, shifting alliances and local wars affected politics and governance. The period predates the outbreak of the Hundred Years' War and the mid-14th-century pandemic known as the Black Death, which would later reshape Europe. Beyond Europe, large polities such as the Mongol successor states, Chinese and Middle Eastern dynasties continued to influence regional affairs, though events varied greatly by region.

Uses and cultural notes

As a practical label, "1332" is commonly used in models, catalog numbers, registry identifiers and addresses with no intrinsic meaning beyond indexing. In mathematical exposition it serves as an example illustrating divisor functions, abundant numbers and factorization properties. Historical references to the year 1332 are used in medieval studies to situate events within the early 14th century.

Notable distinctions

  • Prime factorization: 2^2 × 3^2 × 37.
  • 18 positive divisors; abundant (proper divisors sum to 2,126).
  • Euler totient φ(1332) = 432; refactorable (18 divides 1332).
  • Binary 10100110100, octal 2464, hex 0x534, Roman MCCCXXXII.