Overview

The symbol "56" can denote the integer fifty-six or the calendar year 56 (commonly AD 56). As a number it appears in many mathematical and combinatorial contexts. As a year, it belongs to the first century of the Common Era and sits within the early period of the Roman Empire.

Mathematical properties

Fifty-six has several notable arithmetic and combinatorial features:

  • Factorization: 56 = 2^3 × 7, so it is an even composite number.
  • Divisors: The positive divisors are 1, 2, 4, 7, 8, 14, 28 and 56; the sum of proper divisors exceeds the number, making 56 an abundant number.
  • Figurate numbers: 56 is a pronic number (7×8) and the 6th tetrahedral number, and it also appears as the binomial coefficient C(8,3).

Year AD 56

When used as a year designation, "56" typically refers to AD 56. The year falls in the 1st century; politically it is within the early reign of the Roman emperor Nero. Regional histories also record developments in other parts of Eurasia: imperial China was governed by its ruling dynasty of the period, and early Christian communities were active and spreading across the eastern Mediterranean. For general reference see the entry for year 56 and the broader context of the 1st century.

Element 56: barium

The number 56 is also the atomic number of the chemical element barium (Ba). Barium is an alkaline earth metal used in a variety of industrial and medical applications, often in compound form; for instance, barium sulfate is used in radiographic imaging because it is highly opaque to X-rays.

Notable distinctions and uses

Beyond pure mathematics and historical dating, "56" appears in combinatorics, chemistry, and cultural contexts (for instance model numbers, addresses, or dates). Its mathematical roles—as a pronic, tetrahedral, and binomial-related value—make it a compact example when teaching number classification and combinatorial identities.

Further reading

Readers seeking specialized information can consult subject-specific resources for Roman imperial chronology, elementary number theory, or chemical references on barium. The short label "56" therefore connects diverse topics from arithmetic structure to historical chronology and elemental chemistry.