984 is an integer that sits between 983 and 985. As a number it has standard arithmetic, combinatorial, and numeral-system properties; as a date it denotes a year in the 10th century according to the Julian calendar. The numeral appears in a variety of technical and cultural contexts, from telephone area codes to historical chronologies.

Mathematical properties

In prime-factor terms 984 = 2^3 × 3 × 41. It is an even composite number and has 16 positive divisors. The full list of divisors is: 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984. The sum of all divisors (the sigma function) is 2,520; the sum of proper divisors is 1,536, which exceeds 984 and therefore classifies 984 as an abundant number.

Common numeral representations include binary 1111011000, octal 1730, hexadecimal 3D8, and the Roman numeral CMLXXXIV. Its decimal digit sum is 9+8+4 = 21 (giving a digital root of 3), so it is divisible by 3 but not a Harshad number with respect to the sum of its digits.

Notable arithmetic facts

  • Prime factorization: 2^3 · 3 · 41.
  • Number of divisors: 16.
  • Sum of divisors σ(984) = 2,520, a number that is well known as lcm(1..10).
  • Classification: even, composite, abundant; not a perfect square or triangular number.

Year 984 (AD)

The year 984 falls in the early medieval period. In the Julian calendar it was a leap year. Politically and culturally, the late 10th century saw the consolidation of regional polities across Europe, the continuing Song dynasty rule in China, and shifting dynamics in the Islamic world and Byzantium. In western and central Europe, imperial and royal succession, regencies for child monarchs, and local aristocratic power were typical features of governance at this time.

Uses and other references

Beyond pure mathematics and chronology, the numeral 984 appears in modern identifiers and codes. For example, it is used as a North American telephone area code overlay. Numbers like 984 also occur in product model numbers, catalog entries, and technical specifications where their mathematical properties may be of incidental interest.