80 (eighty) is a natural number that follows 79 and precedes 81. It is an even number and a composite integer commonly written in words as "eighty" or historically as "eight-ten" in some Germanic forms. As a round number in base ten, 80 frequently appears in measurements, percentages (80% = four-fifths), and age descriptions (an octogenarian is someone aged 80–89).
Mathematical properties
In arithmetic, 80 has the prime factorization 2^4 × 5. That factorization explains many of its divisibility properties and its role in base systems that are powers of two or five. It is also an abundant number: the sum of its proper divisors exceeds the number itself.
Important arithmetic functions include Euler's totient φ(80) = 32 and the sum of all positive divisors σ(80) = 186, so the sum of proper divisors is 106, making 80 an abundant number. Its factor structure (2^4 × 5) makes it convenient in fraction reduction and in combinatorial counts involving powers of two.
Representations and notation
Common notations for 80 include Roman numerals LXXX, binary 1010000, octal 120, and hexadecimal 0x50. Written words derive from Old English roots (see below). In measurement systems and everyday use, multiples and factors of 80 often simplify calculations when working with quarters, fifths, or powers of two.
Science and culture: The atomic number 80 identifies the chemical element mercury (Hg) in the periodic table. Historically and linguistically, the English word "eighty" comes from Old English eahta + -tig (eight-tens). In many languages and cultural contexts, 80 serves as a milestone age and a round benchmark for statistics and targets.