| ||||
---|---|---|---|---|
Cardinal | forty-two | |||
Ordinal | 42nd (forty-second) | |||
Factorization | 2 × 3 × 7 | |||
Divisors | 1, 2, 3, 6, 7, 14, 21, 42 | |||
Greek numeral | ΜΒ´ | |||
Roman numeral | XLII | |||
Binary | 1010102 | |||
Ternary | 11203 | |||
Senary | 1106 | |||
Octal | 528 | |||
Duodecimal | 3612 | |||
Hexadecimal | 2A16 |
42 (forty-two) is the natural number that follows 41 and precedes 43.
Forty-two (42) is the sixth pronic number [1] and the eighth abundant number, [2] with an abundance of 12, [3] equal to the average of its eight divisors as an arithmetic number. [4] [5]
Its prime factorization makes it the second sphenic number, and also the second of the form . [6] 42 is the aliquot sum of 30, [7] the smallest sphenic number and second number to have an abundance of 12 after 24, and preceding 42.
It is also the sum of the first six positive non-zero even numbers, , and a Harshad number in decimal, because the sum of its digits is six , which evenly divides 42. [8]
42 itself has an aliquot sum of 54; within an aliquot sequence of twelve composite numbers (42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1) in the prime 3-aliquot tree.
42 is the fifth Catalan number, following 14; consequently, it is [9]
Additionally, 42 is the smallest number that is equal to the sum its non-prime proper divisors; i.e. [10] (with the latter term representing the sixth triangular number). [11]
42 is also the third primary pseudoperfect number, [12] and the first (2,6)-perfect number (super-multiperfect), where [13]
42 is the number of integer partition of 10: the number of ways of expressing 10 as a sum of positive integers. [14] 1111123, one of the forty-two unordered integer partitions of 10, has 42 ordered compositions, since
As a polygonal number, 42 is the first (non-trivial) fifteen-sided pentadecagonal number. [15] It is also the fourth meandric number, [16] and seventh open meandric number [17] (following 8 and 14, respectively).
On the other hand, an angle of 42 degrees can be constructed with a compass and straight edge with the use of the golden ratio; i.e. through the difference between constructible angles of 60 and 18 degrees (with root pentagonal symmetry).
Where the plane-vertex tiling 3.10.15 is constructible through elementary methods, the largest such tiling, 3.7.42, is not. This means that the 42-sided tetracontadigon is the largest such regular polygon that can only tile a vertex alongside other regular polygons, without tiling the plane. [18] [19] [20] [lower-alpha 1]
42 is also the first non-trivial hendecagonal (11-gonal) pyramidal number, after 12. [22] [23] [lower-alpha 2] Otherwise, forty-two is the least possible number of diagonals of a simple convex hendecahedron (or 11-faced polyhedron). [29] [30] [lower-alpha 3]
42 is the only known that is equal to the number of sets of four distinct positive integers — each less than — such that and are all multiples of . Whether there are other values remains an open question. [31]
42 is the resulting number of the original Smith number: Both the sum of its digits, , and the sum of the digits in its prime factorization, , result in 42. [32]
42 is the number of isomorphism classes of all simple and oriented directed graphs on four vertices. [33] I.e., the number of all outcomes (up to isomorphism) of a tournament of four teams where a game between a pair of teams results in three possible outcomes: wins from either team, or a draw. [34]
42 is the fourth Robbins number, equivalently the number of alternating sign matrices. [35] [36] It is also the number of ways to arrange the numbers through in a matrix such that the numbers in each row and column are in ascending order.
42 is the magic constant of the smallest non-trivial magic cube, a cube with entries of 1 through 27, where every row, column, corridor, and diagonal passing through the center sums to forty-two. [37] [38]
42 is the number of (3, 3, 3) standard Young tableaux that use distinct entries [39] [40] [41] (as well as the number of (2, 2, 2, 2, 2) tableaux). [42] [43]
The last natural number less than 100 whose representation as a sum of three cubes was found (in 2019) is forty-two, where, [44]
The 16-dimensional sedenions have 42 "simple" zero divisors of the form where and are unit vectors. [45] [lower-alpha 4] The dimension of the Borel subalgebra in the 6th-dimensional exceptional Lie algebra e6 is 42.
42 is the smallest number such that for every Riemann surface of genus , (by the Hurwitz's automorphisms theorem).
This is related to 42 being the largest where there exist positive integers whose reciprocals alongside that of forty-two generate the sum, [48]
Notice that the first three unit fractions are the first values in the infinite series of Egyptian fractions that most rapidly converges to : see, Sylvester's sequence . [49] The product of the first four terms in Sylvester's sequence is the only number such that is , where represents the -th Bernouilli number. The numbers such that the Bernouilli number has denominator 1806 are
This sequence of numbers are all divisible by 42. [50] 1806 is furthermore the fourth primary pseudoperfect number, following 42. [12] It is the largest primary pseudoperfect number to be the product of consecutive terms in . [lower-alpha 5]
42 is the smallest integer that can only be made from a minimal number of fours (seven) using only addition, subtraction, multiplication, and division, where an intermediate value has to be a non-integer:[ citation needed ]
In decimal representation, the first three digits of pi, , can be arranged as a set of two strings to yield:
In the terminating decimal of the approximation for pi, the string occurs at the 242424th decimal "position" (when treating the decimal point as a position, as well). [51]
PROP. XLII. Blessedness is not the reward of virtue, but virtue itself; neither do we rejoice therein, because we control our lusts, but, contrariwise, because we rejoice therein, we are able to control our lusts. [72]
The number 42 is, in The Hitchhiker's Guide to the Galaxy by Douglas Adams, the "Answer to the Ultimate Question of Life, the Universe, and Everything", calculated by an enormous supercomputer named Deep Thought over a period of 7.5 million years. Unfortunately, no one knows what the question is. Thus, to calculate the Ultimate Question, a special computer the size of a small planet was built from organic components and named "Earth". The Ultimate Question "What do you get when you multiply six by nine" [74] is found by Arthur Dent and Ford Prefect in the second book of the series, The Restaurant at the End of the Universe . This appeared first in the radio play and later in the novelization of The Hitchhiker's Guide to the Galaxy .
The fourth book in the series, the novel So Long, and Thanks for All the Fish , contains 42 chapters. According to the novel Mostly Harmless , 42 is the street address of Stavromula Beta. In 1994, Adams created the 42 Puzzle , a game based on the number 42. Adams says he picked the number simply as a joke, with no deeper meaning.
Google also has a calculator easter egg when one searches "the answer to the ultimate question of life, the universe, and everything." Once typed (all in lowercase), the calculator answers with the number 42. [75]
The novel Catch-22 is written in 42 chapters. Each chapter is named after a character in the book.
The last paragraph of Chapter 1 "The Texan" begins:
In less than ten days the Texan cleared the ward. The artillery captain broke first, and after that the exodus started. [...]
Lewis Carroll, who was a mathematician, [76] made repeated use of this number in his writings. [77]
Examples of Carroll's use of 42:
Dante modeled the 42 chapters of his Vita Nuova on the 42 Stations of the Exodus. [81]
Language | Translation |
---|---|
Afrikaans | twee-en-veertig |
Albanian | dyzetedy |
Arabic | إثنان و أربعون (ʾithnān wa ʾarbaʿūn) |
Armenian | քառասուներկու (karasunerku) |
Armenian (Classic) | ԽԲ (khe ben) |
Basque | berrogeita bi |
Bangla | biyallis ৪২ বিয়াল্লিশ |
Belarusian | сорак два (sorak dva) |
Bosnian | četrdeset dva |
Bulgarian | четиридесет и две (četirideset i dve) |
Catalan | quaranta-dos |
Chinese | 四十二 (肆拾贰) (sìshí'èr) |
Chuvash | хĕрĕх иккĕ (xĕrĕx ikkĕ, IIXXXX) |
Croatian | četrdeset dva |
Czech | čtyřicet dva |
Danish | toogfyrre |
Dhivehi | Saalhees Dheyh |
Dutch | tweeënveertig |
Esperanto | kvardek du |
Estonian | nelikümmend kaks |
Finnish | neljäkymmentäkaksi |
Filipino | apatnapu't dalawa |
French | quarante-deux |
West Frisian | twaenfjirtich |
Galician | corenta e dous |
Georgian | ორმოცდაორი (ormocdaori) |
German | zweiundvierzig |
Greek | σαράντα δύο (saránta dýo) |
Gujarati | betalis |
Hebrew | ארבעים ושתיים (arbayim u-shtayim) |
Hindi | बयालीस, ४२ (bayālīs) |
Hungarian | negyvenkettő |
Icelandic | fjörutíu og tveir |
Indonesian | empat puluh dua |
Irish | daichead a dó |
Italian | quarantadue |
Japanese | 四十二 (よんじゅうに) (yonjūni) |
Kazakh | қырық екі (qırıq eki) |
Korean | 사십이 / 마흔둘 (sasibi/maheundul) |
Kannada | ನಲವತ್ತು ಎರಡು (nalavatthu eradu) |
Latin | quadraginta duo |
Latvian | četrdesmit divi |
Livonian | nēļakimdõ kakš |
Lithuanian | keturiasdešimt du |
Lojban | vore |
Luxembourgish | zweeavéierzeg |
Macedonian | четириесет и два (četirieset i dva) |
Malayalam | നാല്പത്തിരണ്ടു |
Maltese | tnejn u erbgħin |
Māori | whā tekau ma rua |
Marathi | bechalis |
Mongolian | дөчин хоёр (döchin khoyor) |
Norwegian | førtito |
Pashto | دوه څلوېښت |
Persian | چهل و دو (chehel o du) |
Polish | czterdzieści dwa |
Portuguese | quarenta e dois |
Romanian | patruzeci și doi |
Russian | сорок два (sorok dva) |
Sanskrit | द्विचत्वारिंशत्, ४२ (dvicatvāriṃśat) |
Serbian | четрдесет два (četrdeset dva) |
Shona | Makumi mana nemaviri |
Sinhala | හතලිස් දෙක (hathalis deka) |
Slovene | dvainštirideset |
Slovak | štyridsaťdva |
Somali | laba iyo afartan |
Spanish | cuarenta y dos |
Swedish | fyrtiotvå |
Tagalog | apatnapu't dalawa |
Tamil | நாற்பத்திரண்டு (narpatti errundu) |
Telugu | నలభై రెండు (nalabai rendu) |
Thai | สี่สิบสอง |
Turkish | kırk iki |
Ukrainian | сорок два (sorok dva) |
Urdu | بیالیس (bayālīs) |
Vietnamese | bốn mươi hai |
Volapük | foldegtel |
Welsh | pedwar deg dau / dau-ar-ddeugain |
Yoruba | mejilelogoji |
10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.
17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.
21 (twenty-one) is the natural number following 20 and preceding 22.
33 (thirty-three) is the natural number following 32 and preceding 34.
70 (seventy) is the natural number following 69 and preceding 71.
90 (ninety) is the natural number following 89 and preceding 91.
29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime number.
72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or six dozen.
34 (thirty-four) is the natural number following 33 and preceding 35.
48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens.
58 (fifty-eight) is the natural number following 57 and preceding 59.
104 is the natural number following 103 and preceding 105.
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
360 is the natural number following 359 and preceding 361.
144 is the natural number following 143 and preceding 145.
135 is the natural number following 134 and preceding 136.
168 is the natural number following 167 and preceding 169.
177 is the natural number following 176 and preceding 178.
888 is the natural number following 887 and preceding 889.
840 is the natural number following 839 and preceding 841.
Each railway is in a long tunnel, perfectly straight: so of course the middle of it is nearer the centre of the globe than the two ends: so every train runs half-way down-hill, and that gives it force enough to run the other half up-hill.
It is the custom to have no fewer than 48 lines, representing the journeys of Israel, and some say no fewer than 42, because of what God did in the Sinai wilderness at Kadesh. Also, we don't have more than 60 lines, representing the 60 myriads of Israel who received the Torah.
(At the present day the forty-two-lined column is the generally accepted style of the scroll, its length being about 24 inches.)
Media related to 42 (number) at Wikimedia Commons