1149 is a natural number that sits between 1148 and 1150. As an integer it has several elementary arithmetic properties that make it of interest in number theory and recreational mathematics. The label "1149" also denotes years in both the Common Era (AD 1149) and before the Common Era (1149 BC), each occupying distinct places in historical chronologies.

Arithmetic and factorization

In canonical factorization 1149 = 3 × 383, so it is a composite semiprime (product of two primes). Its proper divisors are 1, 3 and 383. The sum of proper divisors is 387, which is less than 1149, so the number is classified as deficient. Because each prime factor occurs with exponent one, 1149 is square‑free.

Numeric functions and representations

  • Euler's totient: φ(1149) = (3−1)(383−1) = 2 × 382 = 764.
  • Sum of all positive divisors (σ): 1 + 3 + 383 + 1149 = 1536, a number equal to 3 × 2^9.
  • Binary: 10001111101; octal: 2175; hexadecimal: 0x47D; Roman numerals: MCXLIX.
  • Because 383 ≡ 3 (mod 4) occurs to an odd power, 1149 cannot be expressed as the sum of two integer squares.

An elementary curiosity: the base‑10 digits of 1149 are 1, 1, 4 and 9, which are the first four perfect squares (1², 1², 2², 3²) when read left to right. Such digit patterns are incidental but make the number visually notable.

Historical years labelled 1149

The designation 1149 may refer to year AD 1149 in the High Middle Ages or to 1149 BC in the Late Bronze Age. AD 1149 falls within a period marked by crusading activity, political consolidation in European states, and developments in monastic and scholastic culture. 1149 BC belongs to an era defined by complex interregional trade and the late phases of Bronze Age civilizations. Specific events tied to those years vary by region and are recorded in specialized historical sources.

As with other integers, 1149 appears in catalogues, indices and identifiers (for example, in technical part numbers, archival references, or sequential lists) where its mathematical properties are incidental to practical labeling. In mathematics it serves as a straightforward example of a semiprime and of how arithmetical functions behave on numbers with small prime factors.