1162 can refer either to the integer that follows 1161 and precedes 1163, or to the year AD 1162 in the medieval Julian calendar. Both senses appear in reference works: the number for mathematical classification and the year for historical chronology. This article treats the number's arithmetic characteristics and summarizes the best documented historical points associated with the year 1162.
Mathematical properties
As an integer 1162 is even and composite. Its prime factorization is 2 × 7 × 83. The full set of positive divisors is 1, 2, 7, 14, 83, 166, 581 and 1162. The sum of these divisors is 2,016, and the sum of proper divisors (excluding 1162 itself) is 854, which makes 1162 a deficient number (the sum of proper divisors is less than the number).
Other notations and encodings include the Roman numeral MCLXII, binary 10010001010, and hexadecimal 0x48A. These representations are commonly used when converting between numeral systems for computing, cryptography examples, or recreational number theory.
Year AD 1162: overview and calendar
In the Julian calendar, AD 1162 was a common year (not a leap year). The twelfth century was a period of dynastic politics, papal influence, and military campaigns in Europe and parts of Asia. Surviving documentary evidence for single years in this era is uneven, but a few widely reported events of 1162 have become standard entries in historical summaries.
Notable events and personages associated with 1162
- Sack of Milan: Imperial forces under Frederick I (Barbarossa) captured and heavily damaged Milan after prolonged conflict with the city; the event figures in accounts of the emperor's effort to assert royal authority in northern Italy.
- Thomas Becket: In 1162 Thomas Becket, then a close associate of King Henry II of England, was elevated to the archbishopric of Canterbury. His appointment marked the start of a famous and ultimately fatal quarrel over ecclesiastical privilege.
- Traditional dating for Genghis Khan: Several later sources and modern traditions place the birth of Temüjin, who became Genghis Khan, around 1162. This date is approximate and debated among historians because contemporary records are scarce.
Context and notable distinctions
When encountering "1162" one should distinguish whether a writer means the numeral, a historical year (AD 1162), or another numbered designation (such as a document, model, or route number). The medieval year should not be confused with 1162 BCE, a separate chronological era whose events belong to the Late Bronze Age and are treated in different reference works.
As both a number and a date, 1162 illustrates how a single sign can carry mathematical properties and serve as a marker in historical timelines. For deeper study, mathematics texts discuss its factorization and classification, while standard medieval histories provide fuller narratives for the events and figures associated with AD 1162.