1086

Year AD 1086 — historical highlights

In England, the Domesday Book was compiled in 1086 on the order of William the Conqueror. Carried out by royal commissioners, the survey recorded landholdings, resources and fiscal obligations across much of England. Because its entries were treated as authoritative and final, later historians and legal scholars have relied on it as a rare, detailed administrative snapshot of the late eleventh-century countryside.

On the Iberian Peninsula, the Battle of Sagrajas (also called Zalaca), fought near Badajoz in 1086, saw the Almoravid forces confront the army of Alfonso VI of León and Castile. The Almoravid commander Yusuf ibn Tashfin intervened at the invitation of some Muslim taifa rulers; his victory checked the recent Christian advance (including Alfonso's capture of Toledo in 1085) and led to greater Almoravid involvement in Iberian affairs.

The year also reflected continuing contestation within the wider Latin Church and among secular rulers: papal and episcopal politics, local reform movements and shifting alliances shaped events across Western Europe. Documentary and administrative developments from 1086 have provided material for a broad range of medieval studies.

Numeric characteristics of 1086

As an integer, 1086 is even and composite. Its prime factorization is 2 × 3 × 181, so it is the product of three distinct primes and qualifies as a sphenic number. It has eight positive divisors: 1, 2, 3, 6, 181, 362, 543 and 1086. The sum of all positive divisors is 2184, so the sum of proper divisors is 1098, which exceeds the number itself and therefore 1086 is classified as an abundant number.

Other common representations: Roman numeral MLXXXVI; binary 10000111110; octal 2076; hexadecimal 43E. Its Euler totient function value is φ(1086) = 360. Because the digital sum is 1+0+8+6 = 15, divisibility by 3 is immediate; the number also illustrates simple multiplicative formulas and divisor-count calculations used in elementary number theory.

Importance and legacy

The events of AD 1086 had lasting influence: the Domesday Book shaped English fiscal administration and land law for generations and remains a crucial primary source for medieval social and economic history. The Battle of Sagrajas influenced the course of the Reconquista by bringing North African Almoravid forces more directly into Iberian politics. As a number, 1086 provides a compact example for teaching factorization, divisor functions, and classifications such as sphenic and abundant numbers.

Notable distinctions

• Year: marked by major administrative and military developments in Western Europe and Iberia.
• Number: 1086 = 2 × 3 × 181; sphenic, abundant, eight divisors, φ(1086)=360; MLXXXVI in Roman numerals.