Overview

116 is a natural even number that follows 115 and precedes 117. It appears in a variety of contexts: as an integer with specific arithmetic properties, as the atomic number for a synthetic chemical element, and as a designation for a historical year and for modern service numbers and roads. The number is common enough to turn up in mathematics, science and everyday labeling.

Mathematical properties

In arithmetic terms, 116 is composite. Its prime factorization is 2^2 × 29, so it has six positive divisors: 1, 2, 4, 29, 58 and 116. The sum of all divisors is 210, and the sum of proper divisors (excluding 116 itself) is 94, which makes 116 a deficient number because 94 < 116. The number of divisors function yields 6 divisors, and Euler's totient function φ(116) = 56.

  • Prime factorization: 2^2 × 29
  • Divisors: 1, 2, 4, 29, 58, 116
  • Proper divisor sum: 94 (deficient)
  • Euler φ: 56
  • Representations: binary 1110100, octal 164, hexadecimal 74, Roman numeral CXVI

Chemical element: atomic number 116

The atomic number 116 corresponds to the synthetic element livermorium (symbol Lv). Livermorium is an extremely radioactive, short-lived element first reported by heavy‑ion collision experiments in the early 21st century; its discovery was the result of collaborative work involving researchers at Dubna and laboratories in the United States. The name "livermorium" and the symbol Lv were adopted by IUPAC to honor the Lawrence Livermore National Laboratory and its contributions to superheavy-element research. Because only a few atoms of livermorium have ever been produced and they decay quickly, chemical and physical properties are inferred from theory and periodic trends; livermorium is placed in group 16 (the chalcogens) and is expected to behave differently from lighter congeners because of strong relativistic effects.

Year 116 (AD) and other cultural uses

The designation 116 also identifies a year in the Common Era. In AD 116 the Roman Empire, under Emperor Trajan, was near the height of its territorial expansion following eastern campaigns. Beyond historical dating, the string "116" is used in modern systems as an identifier: in the European Union telephone numbering plan the prefix 116 is reserved for harmonized helpline numbers of social value (for example, hotlines for missing children or emotional support), and many countries assign the number to roads, bus routes or administrative labels.

Notable facts and distinctions

As an even composite number with a small prime factor (29) and a repeated factor of 2, 116 is structurally simple but finds varied significance depending on context. It is not a square or triangular number; it occupies modest positions in sequences of even numbers and composite numbers. In chemistry, its modern significance comes from representing one of the heaviest elements that have been synthesized and named, while in telecommunications it carries social-service associations through harmonized helpline numbering.

Across mathematics, science and culture, 116 is a clear example of how a single integer can be mapped onto many different domains — from abstract divisor functions to the name of a fleeting, superheavy element, and to an index in modern infrastructure and history.