82 is a natural number that follows eighty-one and precedes eighty-three. It is commonly described as an even number and appears in many numerical contexts. For a simple reference to the numeral itself see 82, and its immediate neighbors are shown by the relationship to 81 and 83.

Mathematical properties

In arithmetic terms, 82 is composite and factors as 2 × 41, making it an even semiprime (a product of two prime numbers). Its positive divisors are listed below, and the sum of its proper divisors shows that 82 is a deficient number.

  • Divisors: 1, 2, 41, 82 — (it is divisible by 1 and by 2 among others)
  • Prime factorization: 2 × 41
  • Sum of proper divisors: 1 + 2 + 41 = 44  (44 < 82, so 82 is deficient)
  • Euler totient: φ(82) = 40
  • Binary: 1010010; Hexadecimal: 52; Roman numerals: LXXXII

As an even integer greater than two, 82 can be expressed as a sum of two primes in accordance with examples predicted by Goldbach-type statements; for instance 82 = 3 + 79. Because it has exactly two prime factors (counted with multiplicity), 82 belongs to the class of semiprimes often studied in elementary number theory.

Occurrence and significance

Outside pure mathematics, the number 82 has clear real-world associations. Most notably, it is the atomic number of the chemical element lead (Pb), a heavy metal with historical and industrial importance. Lead (Z = 82) has been used historically in pipes, pigments and, in modern times, in car batteries and radiation shielding; these uses relate to properties of element 82 rather than to the numeral itself.

Numerals like 82 appear in calendrical and historical notation (years such as 82 BC or AD 82), data labels, addresses, model numbers, and other practical contexts. In recreational number theory and numerology studies one may explore further patterns involving 82, but standard classification relies on the arithmetical facts above.

For quick reference and additional context consult general number resources or encyclopedic entries on integers: basic entry, neighboring values (81, 83), parity classification (even numbers), and divisor information (divisibility by 1, divisibility by 2).