312 is a natural number that follows 311 and precedes 313. In Roman numerals it is written CCCXII. It is an even, composite integer with several simple representations in positional notation: binary 100111000, octal 470 and hexadecimal 0x138.
Mathematical properties
Prime factorization of 312 is 2^3 × 3 × 13, so it has (3+1)(1+1)(1+1) = 16 positive divisors. The sum of all divisors equals 840, giving a sum of proper divisors 528; because the proper divisors sum to more than the number itself, 312 is classified as an abundant number. In base ten it is also a Harshad number, since 312 is divisible by the sum of its digits (3+1+2 = 6).
Years numbered 312
The label 312 identifies years in both the Common Era and before it. The year AD 312 is especially notable in European history for the Battle of the Milvian Bridge, when Constantine I defeated Maxentius. That victory is traditionally associated with Constantine's conversion to Christianity and marked an important turning point in the Roman Empire's religious history. References to 312 BC appear in classical chronologies but are less frequently highlighted in general histories.
Area code and cultural references
As a three-digit sequence, 312 is widely recognized beyond mathematics. In the United States it is a well-known telephone area code that identifies downtown Chicago and parts of the central business district. The number has entered local branding and culture and is used in product names and marketing that play on that geographic identity.
Other uses and distinctions
Numbers such as 312 commonly appear as model numbers, route identifiers, building numbers, or product labels in many countries. Their meaning is determined entirely by context: in mathematics they carry precise arithmetic properties; in history they can indicate a specific year; and in everyday life they serve as short, memorable identifiers for places, services, and brands.