11 (number)

11 (eleven) is the natural number following 10 and preceding 12. It is the smallest number whose name has three syllables.

Natural number

| <- 10  | 11 |  12 ->

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← 10 11 12 13 14 15 16 17 18 19 →

* List of numbers
* Integers

← 0 10 20 30 40 50 60 70 80 90 →

Cardinal| eleven
Ordinal| 11th
(eleventh)
Numeral system| undecimal
Factorization| prime
Prime| 5th
Divisors| 1, 11
Greek numeral| ΙΑ´
Roman numeral| XI, xi
Greek prefix| hendeca-/hendeka-
Latin prefix| undeca-
Binary| 10112
Ternary| 1023
Senary| 156
Octal| 138
Duodecimal| B12
Hexadecimal| B16
Bangla| ১১
Hebrew numeral| י"א
Devanagari numerals| ११
Malayalam| ൰൧
Tamil numerals| கக
Telugu| ౧౧
Babylonian numeral| 𒌋𒐕

## Name

[edit]

"Eleven" derives from the Old English ęndleofon, which is first attested in Bede's late 9th-century Ecclesiastical History of the English People.[2][3] It has cognates in every Germanic language (for example, German elf), whose Proto-Germanic ancestor has been reconstructed as *ainalifa-,[4] from the prefix *aina- (adjectival "one") and suffix *-lifa-, of uncertain meaning.[3] It is sometimes compared with the Lithuanian vienúolika, though -lika is used as the suffix for all numbers from 11 to 19.[3]

The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as *ainlifun. This was formerly thought to be derived from Proto-Germanic *tehun ("ten");[3][5] it is now sometimes connected with *leikʷ- or *leip- ("left; remaining"), with the implicit meaning that "one is left" after counting to ten.[3]

## Mathematics

[edit]

11 is a prime number, and a super-prime. 11 forms a twin prime with 13,[6] and sexy pair with 5 and 17. 11 is also the first prime exponent that does not yield a Mersenne prime. 11 is part of a pair of Brown numbers. Only three such pairs of numbers are known.[7] Rows in Pascal's triangle can be seen as representation of powers of 11.[8]

### Geometry

[edit]

Copper engraving of a hendecagon, by Anton Ernst Burkhard von Birckenstein (1698)

An 11-sided polygon is called a hendecagon, or undecagon. A regular hendecagon is the polygon with the fewest number of sides that is not able to be  constructed with a straightedge, compass, and angle trisector.[9]

The Mathieu group M 11 {\displaystyle \mathrm {M} _{11}} is the smallest of twenty-six sporadic groups. It has order 7920 = 2 4 ⋅ 3 2 ⋅ 5 ⋅ 11 = 8 ⋅ 9 ⋅ 10 ⋅ 11 {\displaystyle 7920=2^{4}\cdot 3^{2}\cdot 5\cdot 11=8\cdot 9\cdot 10\cdot 11} , with 11 as its largest prime factor.  M 11 {\displaystyle \mathrm {M} _{11}} is the maximal subgroup Mathieu group  M 12 {\displaystyle \mathrm {M} _{12}} , where 11 is also its largest prime factor.[citation needed]

### List of basic calculations

[edit]

Multiplication | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10  | 11  | 12  | 13  | 14  | 15  | 16  | 17  | 18  | 19  | 20  | 25  | 50  | 100  | 1000

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11 × x | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 | 143 | 154 | 165 | 176 | 187 | 198 | 209 | 220 | 275 | 550 | 1100 | 11000
Division | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10  | 11  | 12  | 13  | 14  | 15

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11 ÷ x | 11 | 5.5  | 3.6 | 2.75  | 2.2  | 1.83 | 1.571428 | 1.375  | 1.2 | 1.1  | 1  | 0.916 | 0.846153 | 0.7857142 | 0.73
x ÷ 11 | 0.09 | 0.18 | 0.27 | 0.36 | 0.45 | 0.54 | 0.63 | 0.72 | 0.81 | 0.90 | 1 | 1.09 | 1.18 | 1.27 | 1.36
Exponentiation | 1  | 2  | 3  | 4  | 5  | 6  | 7  | 8  | 9  | 10  | 11

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11x | 11 | 121  | 1331  | 14641  | 161051  | 1771561  | 19487171  | 214358881  | 2357947691  | 25937424601  | 285311670611
x11 | 1  | 2048  | 177147  | 4194304  | 48828125  | 362797056  | 1977326743  | 8589934592  | 31381059609  | 100000000000  | 285311670611

## Music

[edit]

See also: Eleven (disambiguation) § Music

The interval of an octave plus a fourth is an 11th. A complete 11th chord has almost every note of a diatonic scale.

## Cultural references

[edit]

### Film

[edit]

In the mockumentary film This Is Spinal Tap, the idiomatic phrase up to eleven is coined to allude to going beyond the limitations of a system, in this case music amplifier volume levels.

### "Eleventh hour"

[edit]

Being one hour before 12:00, the eleventh hour means the last possible moment to take care of something, and often implies a situation of urgent danger or emergency (see Doomsday clock). "The eleventh hour" is a phrase in the Parable of the Workers in the Vineyard in the Bible.

### Eleventh Night

[edit]

Main article: Eleventh Night

In protestant communities in Northern Ireland bonfires are lit to mark the eve of protestant William III of England victory over the catholic James II of England at the battle of the Boyne

## Languages

[edit]

While 11 has its own name in Germanic languages such as English, German, or Swedish, and some Latin-based languages such as Spanish, Portuguese, and French, it is the first compound number in many other languages: Chinese 十一 shí yī, Korean 열하나 yeol hana or 십일 ship il.

## Mysticism

[edit]

The number 11 (alongside its multiples 22 and 33) are master numbers in numerology, especially in New Age.[10]

## Religion

[edit]

The Quran refers to the number eleven in Surah Yusuf, verse 4:[11]

> ˹Remember˺ when Joseph said to his father, “O my dear father! Indeed I dreamt of eleven stars, and the sun, and the moon—I saw them prostrating to me!”

The dream came true at the end of the story when Yusuf's eleven brothers and parents prostrated before him in Egypt.[12]

In the Bible, Joseph has 11 brothers.

## References

[edit]

1. ^ Bede, Eccl. Hist., Bk. V, Ch. xviii.
2. ^ Specifically, in the line Osred ðæt rice hæfde endleofan wintra.[1]
3. ^ a b c d e Oxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891.
4. ^ Kroonen, Guus (2013). Etymological Dictionary of Proto-Germanic. Leiden: Brill. p. 11f. ISBN 978-90-04-18340-7.
5. ^ Dantzig, Tobias (1930), Number: The Language of Science.
6. ^ Sloane, N. J. A. (ed.). "Sequence A001359 (Lesser of twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-22.
7. ^ Weisstein, Eric W. "Brocard's Problem". MathWorld. Retrieved 24 July 2025.
8. ^ Mueller, Francis J. (1965). "More on Pascal's Triangle and powers of 11". The Mathematics Teacher. 58 (5): 425–428\. doi:10.5951/MT.58.5.0425. JSTOR 27957164.
9. ^ Gleason, Andrew M. (1988). "Angle trisection, the heptagon, and the triskaidecagon". American Mathematical Monthly. 95 (3). Taylor & Francis, Ltd: 191–194\. doi:10.2307/2323624. JSTOR 2323624. MR 0935432. S2CID 119831032.
10. ^ Sharp, Damian (2001). Simple Numerology: A Simple Wisdom book (A Simple Wisdom Book series). Red Wheel. p. 7\. ISBN 978-1-57324-560-9.
11. ^ "Surah Yusuf - 4". Quran.com. Retrieved 2025-06-23.
12. ^ "Surah Yusuf - 100". Quran.com. Retrieved 2025-06-23.

## External links

[edit]

Wikimedia Commons has media related to 11 (number).

Grimes, James. "Eleven". Numberphile. Brady Haran. Archived from the original on 2017-10-15. Retrieved 2016-01-03.

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* 10,000
* 16,807
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* 64,079
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* 100,000
* 142,857
* 144,000
* 1,000,000
* 10,000,000
* 43,112,609
* 100,000,000
* 1,000,000,000
* 2,147,483,647
* 4,294,967,295
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* 100,000,000,000

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