1335 (number and year)

1335 is an odd composite integer (3·5·89), a sphenic and squarefree number with φ(1335)=704 and σ(1335)=2160; it also denotes the year MCCCXXXV in the 14th century, before the Black Death and the Hundred Years' War.

1335 is a natural number that follows 1334 and precedes 1336. As a decimal integer it is odd and composite; in Roman numerals it is written MCCCXXXV. The symbol 1335 serves in mathematics to denote an integer with specific arithmetic and number‑theoretic properties and outside mathematics as a simple numerical identifier for years, catalog entries, models and records.

Mathematical properties

Numerically, 1335 factors as 3 × 5 × 89. Because it is the product of three distinct primes it is a sphenic number and is squarefree. It has eight positive divisors in total. The sum of all divisors is σ(1335) = 2160 and the sum of proper divisors is 825, which is less than 1335, so the number is deficient.

Prime factors: 3, 5, 89
Divisors: 1, 3, 5, 15, 89, 267, 445, 1335
Number of divisors τ(1335) = 8; Euler totient φ(1335) = 704
Base representations: binary 10100110111; octal 2467; hexadecimal 0x537
Digit sum: 1+3+3+5 = 12 (divisible by 3)

Because one of its prime factors, 89, is itself a prime that appears in the Fibonacci sequence, 1335 can be seen as combining small primes with a larger prime of particular interest in other contexts. It is not a perfect power, nor a prime, and it is coprime to many smaller integers according to its totient value.

1335 as a calendar year (MCCCXXXV)

When read as a year, 1335 falls in the first half of the 14th century. It precedes two major mid‑century developments in European history: the Black Death, commonly dated from c.1347 to 1351, and the wider outbreak of the Hundred Years' War, conventionally beginning in 1337. Single medieval years like 1335 are best understood via regional chronicles and records: political disputes, local wars, dynastic successions and legal actions were common, and surviving documentation varies between regions and languages.

As with many ordinary integers, 1335 is used as a neutral identifier in lists, archival systems, product model numbers and administrative codes. In such uses its mathematical properties are incidental to its role as a compact numeric label.