1088 (integer and year)

Mathematical properties

In arithmetic 1088 is an even composite integer. Its prime factorization is 2^6 × 17, which makes it a product of a power of two and an odd prime. Because of that decomposition it can be written as 64 × 17 and also equals 33^2 − 1 (one less than the perfect square 33²), which factors as 32 × 34.

• Prime factorization: 2^6 · 17
• Number of positive divisors: 14
• Sum of all divisors: 2,286; sum of proper divisors: 1,198 (so 1088 is an abundant number)
• Representations: binary 10001000000₂; octal 2100₈; hexadecimal 0x440

The full set of positive divisors is: 1, 2, 4, 8, 16, 32, 64, 17, 34, 68, 136, 272, 544, 1088. Because the sum of its proper divisors exceeds the number itself, 1088 is classified as abundant rather than perfect or deficient.

Year AD 1088: historical context

The designation 1088 AD places the year within the High Middle Ages. In Western Europe this era followed the Norman Conquest of England (1066) and saw consolidation of feudal monarchies, disputes over church and secular authority, and frequent noble revolts. One notable episode often dated to this time is a baronial revolt in England and Normandy that tested the authority of William II and other rulers; such uprisings were part of the broader political instability of the period. Elsewhere, contemporary states and empires across Europe, the Middle East, and East Asia continued administrative, cultural, and military developments characteristic of the 11th century.

When the year is written in Roman numerals it appears as MLXXXVIII. As a chronological label it is used in historical timelines, primary-source citations, and inscriptions that denote events of that calendar year.

Uses, occurrences, and notable facts

Outside pure mathematics and historical dating, the symbol 1088 appears in technical contexts where integers express sizes, addresses, or counts: for example in computing as a numeric value or identifier, and in engineering or catalog numbers. Its tidy factorization (a high power of two times a small prime) and its representation 0x440 in hexadecimal make it convenient in binary and low-level programming contexts. Numerically, being one less than a square (33² − 1) and equal to 2^6·17 gives it simple factorizations that can be useful in algebraic manipulations and problem examples.

Summary: 1088 is a composite, even, abundant number with a compact prime factorization and clear base representations; as a year it falls in a formative century of medieval history and is used as a chronological reference in historical study.