Number reference
11 explained.
11: eleven, prime, repdigit; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- eleven
- Classification
- prime
- Factors
- 1, 11
- Prime factorization
- 11
- Square root
- 3.316625
- Cube root
- 2.22398
- Binary
- 1011
- Octal
- 13
- Hexadecimal
- B
- Roman numeral
- XI
- Digit sum
- 2
- Digital root
- 2
What makes 11 notable
- Prime. 11 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
- Repdigit. 11 is written with a single repeated digit, so it is divisible by the repunit of the same length.
- Palindromic prime. 11 is prime and reads the same forwards and backwards.
11 in everyday use
Eleven players make up a side in football, cricket, field hockey, and American football. It is the atomic number of sodium, and Apollo 11 carried the first astronauts to the Moon in July 1969. The First World War armistice took effect at eleven o'clock on the eleventh day of the eleventh month, 1918, and that hour is still observed. The English word comes from Old English for "one left" — one left over after counting to ten. An amplifier that "goes to eleven" is a joke from the 1984 film This Is Spinal Tap.
Eleven is the fifth prime and the smallest two-digit prime, a palindrome, and the first of a twin-prime pair with 13. Multiplying a two-digit number by 11 has a shortcut: add the digits and put the sum in the middle, so 11 × 11 = 121 and 11 × 23 = 253. To test divisibility, alternately add and subtract the digits; if the result divides by 11, so does the number.
Nearby numbers
How to read this page
Because 11 is prime, the factor list stops at 1 and 11 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 11 in its prime factorisation inherits it from here.
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