1364

1364 — an integer with distinct arithmetic features and a calendar year in the mid-14th century; this article outlines its mathematical properties, common representations, and historical context.

1364 is both a natural number and a year in the 14th century. As an integer it sits between 1363 and 1365; as a calendar year (AD 1364) it belongs to a period marked by political fragmentation, demographic recovery after the Black Death, and ongoing conflicts such as the Hundred Years' War. The dual identity of "1364" makes it a useful reference point in numerical, historical and cultural discussions.

Mathematical properties

In arithmetic, 1364 is an even composite number. Its prime factorization is 2² × 11 × 31, which yields a total of 12 positive divisors. The sum of all divisors is 2688, and the sum of proper divisors (1324) is less than the number itself, so 1364 is a deficient number. It is not a perfect square, not triangular, and does not appear among the Fibonacci numbers.

Prime factors: 2² × 11 × 31
Divisors: 1, 2, 4, 11, 22, 44, 31, 62, 124, 341, 682, 1364
Binary: 10101010100
Hexadecimal: 0x554
Roman numeral: MCCCLXIV

Because of its factor pattern it is easy to work with in modular arithmetic and combinatorial counting problems that involve grouping into factors of 2, 11 or 31. Its alternating-bit binary pattern (10101010100) is visually regular, which sometimes attracts attention in recreational number discussion.

1364 as a historical year

Year 1364 falls in the middle of the 14th century, a transitional era in many regions. Europe was still coping with the demographic, economic and social consequences of the mid-century plague outbreaks; political powers were reshaping boundaries through dynastic succession and military campaigns. The Avignon Papacy influenced church politics while universities and courts continued to develop administrative practices that would shape later nation-states.

Beyond Europe, established empires and states in Asia, North Africa, and the Americas pursued their own trajectories of trade, warfare, and cultural production. Records from individual polities differ in detail and survival, so the specific events attached to the year 1364 vary by region and source.

In modern usage, 1364 appears in catalogues, model numbers, addresses and archival citations; as both a numeral and a year it functions as an organizational label. Its clear factorization and concise digital representations make it convenient for computational examples and classroom illustrations of divisor functions, number bases, and calendar-era discussions.