Overview
The integer 18 (eighteen) is the natural number following 17 and preceding 19. It is even and composite, with a simple decimal notation "18". As a common counting number it appears across mathematics, science and everyday life. For a basic definition of number concepts see number.
Mathematical characteristics
Key arithmetic facts about 18: its prime factorization is 2 × 3², so it is not square-free. The positive divisors of 18 are 1, 2, 3, 6, 9 and 18. Because the sum of its proper divisors (1+2+3+6+9 = 21) exceeds 18, it is classified as an abundant number. Euler's totient function yields φ(18) = 6. The sum of all divisors is 39. 18 is semiperfect (some proper divisors add to it exactly) and is divisible by 2, 3, 6, and 9.
Representations and sequences
Common numeral system representations include binary 10010, octal 22 and hexadecimal 12. In Roman numerals 18 is written XVIII. Multiples of 18 form an infinite arithmetic progression: 18, 36, 54, 72, 90, 108, … . Its position in integer sequences makes it a frequent example when illustrating divisibility, modular arithmetic and factorization.
Uses, examples and importance
Beyond pure mathematics, 18 appears repeatedly in culture and science. It is the atomic number of argon, a noble gas important in lighting and inert atmospheres. In many legal systems 18 is the benchmark for adulthood—often the age of majority, eligibility to vote, and the threshold for other civic rights (exact rules vary by jurisdiction). In sport and recreation, many modern golf courses are arranged with 18 holes, a standard that has become globally recognized.
History, symbolism and notable facts
Historically the number has been represented in various numeral systems; the Roman form XVIII remains familiar. Culturally, in Judaism the numerical value of the word "chai" (life) is 18, giving the number symbolic significance and a custom of gifting in multiples of 18. Other ordinary facts include its evenness and role as a useful composite example in elementary number theory. For a note on even numbers in general see even number.
Summary
18 is a small but richly connected integer: mathematically instructive because of its factorization and divisor properties, scientifically meaningful as argon's atomic number, and culturally prominent through legal age conventions and symbolic uses. Its simple structure makes it a useful teaching example for divisibility, representations and classification within the integers.