1168 is an integer that can be considered both as a pure number and as the label for a year in the 12th century. In Roman numerals it is written MCLXVIII. As a year under the Julian calendar it belongs to the later part of the High Middle Ages, a period marked by political change, religious movements and cultural developments across Europe, the Middle East and East Asia.

Mathematical properties

As an integer, 1168 is even and composite. Its prime factorization is 24 × 73, which explains several of its elementary properties. The full list of positive divisors is:

  • 1, 2, 4, 8, 16, 73, 146, 292, 584, 1168

From this factorization one can compute standard arithmetic functions: the number of divisors is 10, the sum of all divisors is 2294, and the sum of proper divisors is 1126, so 1168 is a deficient number (its proper divisors sum to less than the number). Its Euler totient is φ(1168) = 576.

Representations and notable numeric facts

1168 has several compact representations: in binary it is 10010010000, and in hexadecimal it is 0x490. It is a Harshad number in base 10 because it is divisible by the sum of its digits (1+1+6+8 = 16, and 1168 ÷ 16 = 73). A classical geometric observation follows from its factorization: since 73 = 8² + 3², multiplying by 16 = 4² yields 1168 = 32² + 12², so it can be expressed as the sum of two squares.

The year 1168 in historical perspective

The calendar year 1168 falls in the High Middle Ages, a time of active political, religious and cultural realignment. Across Europe, feudal principalities, emerging monarchies and ecclesiastical institutions interacted through alliances, conflicts and reform movements. In the eastern Mediterranean the Crusader states continued to shape relations between Latin Christendom and various Muslim polities. In East Asia, the Song dynasty in China and rival dynasties in neighboring regions were centres of technological and commercial development. Surviving chronicles, legal documents and architectural remains from this era reflect local events—such as successions, military actions and church affairs—rather than a single global narrative.

Cultural uses and distinctions

Outside strict mathematics or calendrical usage, the number 1168 appears as an identifier in administrative records, catalog numbers, model designations and addresses—roles typical for four-digit integers. Its mathematical features (a power-of-two factor times a prime, expressibility as a sum of two squares, Harshad property) make it a useful small example in elementary number theory classes when illustrating factorization, divisor functions and classical representations.

Overall, 1168 illustrates how a single numeral can be examined from multiple angles: as an object with concrete arithmetic properties and as a chronological label that anchors attention to a historical period with diverse local developments rather than a single defining event.