11 (number)

11 is a natural number that follows 10 and precedes 12. It is written using two digits, both of which are 1. It is the first two-digit number that cannot be written as a single digit in the base-10 system after 10.

In mathematics, 11 is a prime number — it is divisible only by 1 and itself. It is the fifth prime number, after 2, 3, 5, and 7. It is also an odd number and is not divisible by 2.

Mathematical properties

11 is the only two-digit prime number in the base-10 system. There is a well-known divisibility rule: a number is divisible by 11 if the alternating sum of its digits (adding and subtracting digits alternately) is divisible by 11. Example: 121 = 11 × 11. Additionally, 11 is the base for repunit numbers — numbers whose digits are all 1, such as 11, 111, and 1111.

Multiplication of 11 produces recognizable patterns: 11 × 11 = 121, 11 × 12 = 132. In geometry, 11 is also the number of sides of the shape called a hendecagon.

Common usage

In time measurement systems, 11 is the hour before 12. In team sports, an outdoor football team consists of 11 players, which is why the number 11 is strongly associated with that sport. In addition, the ISBN-10 check-digit system uses modulo 11 arithmetic to verify the validity of a book number.

In other base systems, 11 in base 10 is written as 1011 in binary and B in hexadecimal. In base 11, it is written as 10.