Overview
1106 is a natural number that follows 1105 and precedes 1107. It is most often discussed in two contexts: as an integer with specific arithmetic properties, and as the designation of a year in the early 12th century (AD 1106). Both senses appear in mathematics, chronology, and historical summaries.
Mathematical characteristics
Arithmetically, 1106 is an even composite integer. Its prime factorization is 2 × 7 × 79, so it is the product of three distinct primes (squarefree). The positive divisors of 1106 are 1, 2, 7, 14, 79, 158, 553 and 1106. The sum of the proper divisors is 814, which is less than 1106, so the number is classified as deficient.
- Euler totient: φ(1106) = 468.
- Binary representation: 10001010010.
- Hexadecimal: 0x452.
- Roman numerals: MCVI.
Historical year AD 1106
The year 1106 (MCVI) falls in the High Middle Ages. One of its best known events is the Battle of Tinchebray, in which King Henry I of England defeated his elder brother Robert Curthose, Duke of Normandy; Robert was captured and held for many years, consolidating Henry's control over Normandy. The year also belongs to a period of feudal consolidation, dynastic rivalry and reform movements across Europe and the Near East.
Uses and notable distinctions
As with many integers, 1106 appears in straightforward ways: serial numbers, designations, model numbers, and dates. In number theory it serves as a simple example of a squarefree composite number with three prime factors, useful when illustrating multiplicative functions (for example, calculating φ(n) or σ(n)). As a calendar year it is commonly referenced in medieval English and Norman histories because of its political consequences.
Summary
1106 combines modest mathematical interest—an even, squarefree, deficient composite—with a recognizable historical footprint as a year marked by military and dynastic events. Whether studied numerically or historically, it provides clear, concrete examples in both domains.