Overview
Eleven is the integer after ten and before twelve. It is an ordinary number used in counting and measurement, written as 11 in Hindu–Arabic numerals and as XI in Roman numerals. In spoken English it is typically pronounced "eleven." Eleven is odd and cannot be divided evenly by 2.
Mathematical properties
Eleven is a prime number: its only positive divisors are 1 and itself, so it follows the sequence 2, 3, 5, 7, 11 of early primes. It is also a member of several special classes of primes: 11 forms a twin prime pair with 13, is a safe prime (since (11−1)/2 = 5 is prime), and is a Sophie Germain prime (because 2·11+1 = 23 is prime). In base ten it is the smallest two-digit palindromic prime.
A useful arithmetic rule: a decimal number is divisible by 11 when the alternating sum of its digits is a multiple of 11 (for example, 2728 → 2−7+2−8 = −11, so 2728 is divisible by 11). In binary, eleven is written 1011.
History and etymology
The English word "eleven" derives from Old English forms related to a Germanic root meaning "one left (after ten)." Many languages preserve a separate term for eleven rather than forming it by combining ten and one. The name of the month November reflects earlier Roman calendars where it was the ninth month; after reforms it became the eleventh month but retained its original name.
Uses, examples, and cultural notes
Eleven appears in science as the atomic number of sodium. It is the number of players on a traditional association football (soccer) team and on a cricket side. In everyday culture, "the eleventh hour" denotes a last moment before a deadline. In games, sports and music the number often marks formations, positions, or scales.
Because of its simple digit pattern, 11 is used in tests, codes, and puzzles; its divisibility rule is a standard classroom example. For more on the concept of number, the distinction of odd numbers, and primality, see related entries: number, odd number, prime number.