1145 is both an integer and a calendar year. As a number it has several elementary arithmetic and number‑theoretic properties; as a year (1145 CE) it lies in the high Middle Ages, a period of religious, political and intellectual change in Europe and continued activity across Eurasia.

Mathematical properties

Factorization: 1145 = 5 × 229, so it is a semiprime (the product of two distinct primes) and therefore squarefree. Its positive divisors are 1, 5, 229 and 1145; the sum of all divisors is 1 + 5 + 229 + 1145 = 1380. The sum of proper divisors (1 + 5 + 229 = 235) is less than 1145, so the number is deficient.

  • Number of divisors τ(1145) = 4.
  • Euler's totient φ(1145) = (5−1)(229−1) = 4 × 228 = 912.
  • Möbius function μ(1145) = (−1)2 = +1, since it is a product of two distinct primes.
  • Representations: binary 10001111001, octal 2171, hexadecimal 0x479, Roman numeral MCXLV.
  • Sum of two squares: because both prime factors (5 and 229) are sums of two squares, 1145 can be expressed as 11² + 32² = 121 + 1024 = 1145, a simple example of the two‑squares theorem in practice.

Its elementary semiprime form makes 1145 a convenient example in introductory discussions of factorization, multiplicative arithmetic functions and representations by quadratic forms.

1145 CE in context

The year 1145 falls in the high Middle Ages. It follows close after the 1144 fall of Edessa, an event that helped prompt renewed calls for military expeditions from Western Christendom and contributed to the mobilization known as the Second Crusade (launched a few years later). The mid‑twelfth century more broadly saw ongoing consolidation of principalities, reform movements within monasticism and the church, the growth of cathedral schools that would evolve into universities, and expanding urban and commercial activity across Europe.

Beyond Europe, the twelfth century was a dynamic era in the Islamic world, the Byzantine Empire and Song‑period China. While 1145 itself is not commonly associated with a single universally defining global event, it is typical of a century marked by political realignments, cultural exchanges and developments in learning, law and trade that shaped later medieval society.

Uses and distinctions

  • As an identifier: 1145 is used in catalogues, model numbers, addresses and route designations.
  • Educationally: it serves as a straightforward semiprime example for exercises in factorization, totient calculation and representations as sums of squares.