Overview

1155 is an integer that appears in mathematical classification, historical chronology and modern product and model naming. As an arithmetic object it is a composite, squarefree odd number with a straightforward prime factorization. As a label it denotes calendar years in both the common era and the pre‑common era, and it is used in industry as an identifier for sockets, parts and regulations.

Mathematical properties

In prime factor terms, 1155 = 3 × 5 × 7 × 11, the product of four distinct primes. Because each prime factor occurs only once, 1155 is squarefree. The number of positive divisors is 2^4 = 16. The sum of all positive divisors (the sigma function) equals (1+3)(1+5)(1+7)(1+11) = 2,304, so the sum of proper divisors is 2,304 − 1,155 = 1,149. That value is less than 1,155, which makes 1155 a deficient number. The Euler totient function equals 1155 × (1−1/3)×(1−1/5)×(1−1/7)×(1−1/11) = 480, so there are 480 integers less than 1155 that are coprime to it.

The complete list of positive divisors is: 1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 77, 105, 165, 231, 385 and 1155. Because of its factorization into four distinct primes, 1155 is not a sphenic number (sphenic numbers have exactly three distinct prime factors) and is an odd composite number rather than prime or a prime power.

1155 in history

The notation "1155" can refer to the year AD 1155, in the middle of the 12th century, a period of active political and ecclesiastical developments in medieval Europe. A widely cited event from that year is the imperial coronation of Frederick I, known as Barbarossa, as Holy Roman Emperor. The label may also refer to 1155 BC, a date within the late Bronze Age when surviving records are sparser and specific events are often uncertain; many ancient chronologies for that era are approximate.

Modern uses and common references

Beyond pure arithmetic and historical dating, 1155 is commonly used as a model, part or catalogue number. A prominent technical use is Intel's LGA 1155 (Socket H2), a desktop CPU socket associated with Intel's second and third generation Core processor families. More generally, the sequence 1155 appears in road numbers, legal citations, product model numbers and other indexing schemes, where it serves as an identifier rather than conveying intrinsic mathematical meaning.

Summary

  • 1155 = 3 × 5 × 7 × 11, an odd, squarefree composite integer.
  • It has 16 positive divisors; the sum of divisors is 2,304 and the sum of proper divisors is 1,149 (deficient).
  • As a year, AD 1155 is a noted date in medieval European history; 1155 BC falls in the late Bronze Age.
  • In technology and commerce, 1155 commonly appears in model and socket names such as LGA 1155.