Overview

1104 is a natural number that follows 1103 and precedes 1105. It appears both as an ordinal integer and as a calendar year (AD 1104). As an ordinary composite even number, it has a handful of elementary arithmetic properties of interest in number theory and practical numeration systems.

Mathematical properties

In prime factorization 1104 = 2^4 × 3 × 23. From this follow several standard arithmetic functions: it has 20 positive divisors, Euler's totient phi(1104) = 352, and the sum of all divisors sigma(1104) = 2976, which makes the sum of proper divisors 1872. Because this exceeds the number itself, 1104 is classified as an abundant number.

Common numeral representations include binary 10001010000, octal 2120, and hexadecimal 0x450. In Roman numerals 1104 is written MCIV. It is divisible by 16, 3 and 23, and can be expressed as 16×69 or 48×23.

Year AD 1104

The year 1104 (MCIV) belongs to the early 12th century in the medieval period and was treated as a leap year in the Julian calendar used at the time. One of the most frequently cited events of AD 1104 is the Battle of Harran, a major clash between Crusader forces from the County of Edessa and Antioch and their Muslim opponents; the engagement is often noted as a serious setback for the Crusader states in the Levant.

Notable facts and uses

  • 1104 occurs as a label or identifier in modern contexts: product and model numbers, route numbers, and archival references commonly use four-digit sequences like 1104.
  • Mathematically, its structure (a small power of two times two distinct odd primes) makes it a convenient example when illustrating divisor functions, multiplicative arithmetic functions, and abundant numbers.
  • As a calendar year, 1104 sits within a period of political and religious change in Europe and the Near East, often invoked in surveys of the Crusades and medieval chronology.

Though not remarkable for containing famous mathematical constants or being prime, 1104 serves as a clear, concrete example in elementary number theory and as a useful chronological marker in medieval history.