1184 (number and year)

Mathematical properties

As an integer, 1184 factors as 2^5 × 37. It has twelve positive divisors: 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 and 1184. The sum of all divisors (the divisor function σ) equals 2,394, so the sum of proper divisors is 1,210. Because the sum of its proper divisors exceeds the number itself, 1184 is an abundant number.

1184 and 1210 form an amicable pair: each number equals the sum of the proper divisors of the other. This pair is the second-smallest amicable pair after (220, 284) and is often cited in introductory discussions of amicable numbers and number theory.

Historical and chronological notes

When used as a year number, "1184" can indicate very different contexts. Classical chronographers such as Eratosthenes and later ancient tradition sometimes assign the fall of Troy to about 1184 BC; this is a traditional, not unanimously accepted, date for the legendary event. In AD 1184, northern European history includes episodes of dynastic and naval warfare—one well-documented occurrence that year was the Battle of Fimreite in Norway, where competing claimants to the throne fought a decisive engagement.

Uses and significance

• In recreational mathematics and number theory, 1184 is used as a standard example of an even abundant amicable number.
• As a historical label, the year appears in chronologies of medieval Europe and in ancient chronicle traditions about the late Bronze Age Mediterranean.

Notable facts

Because of its simple factorization and small set of divisors, 1184 is easy to work with in divisor-sum calculations and in demonstrations of amicable-number properties. Its role in chronology is primarily traditional or regional rather than globally pivotal: different cultures record different events for their local year 1184.