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888 (number)

From Wikipedia, the free encyclopedia
For other uses, see888 (disambiguation).
Natural number
← 887888 889 →
Cardinaleight hundred eighty-eight
Ordinal888th
(eight hundred eighty-eighth)
Factorization23 × 3 × 37
Greek numeralΩΠΗ´
Roman numeralDCCCLXXXVIII,dccclxxxviii
Binary11011110002
Ternary10122203
Senary40406
Octal15708
Duodecimal62012
Hexadecimal37816

888 (eight hundred eighty-eight) is thenatural number following887 and preceding889.

It is astrobogrammatic number that reads the same right-side up and upside-down on a seven-segment calculator display,symbolic in variousmystical traditions.

In mathematics

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888 is abase tenrepdigit (a number all of whose digits are equal),[1] and

888=24×37.{\displaystyle 888=24\times 37.}

Where37 is the 12th prime number.

888 is apractical number, meaning that every positive integer up to 888 itself may be represented as a sum of distinctdivisors of 888.[2]

888 is a Harshad number as it is divisible by its sum of digits, where 888 ÷ (8, 8, 8) is 888 ÷ 24, an equivalent fraction to 444 ÷ 12 or 222 ÷ 6, which is37.

888 is equal to the sum of the first twoGiuga numbers:30 +858 = 888.[3]

There are exactly:

Crystagon

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888 is also the 16th area of acrystagon, equivalent with the quotient ofbinomial coefficientC(7n,2){\displaystyle \mathrm {C} (7n,2)} and7{\displaystyle 7} withn=16{\displaystyle n=16}.[7][8]

This property permits 888 to be equivalent with:[7]

Heronian tetrahedron

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888 is the 42nd longest side of aHeronian tetrahedron,[9] whoseedge lengths, faceareas andvolumes are allintegers; more specifically it is the second-largest longest side of a primitive Heronian tetrahedron (after203, and preceding1804)[a] with four congruent trianglefaces (thisprimitive Heronian tetrahedron is a tetrahedron where four edges share no commonfactor).[18]

Decimal properties

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888 is the smallest multiple of twenty-four divisible by all of its digits,[19] whosedigit sum is also itself.[20]

It is ahappy number indecimal, meaning that repeatedly summing the squares of its digits eventually leads to 1:

88864+64+64=1921+81+4=8664+36=1001.{\displaystyle 888\mapsto 64+64+64=192\mapsto 1+81+4=86\mapsto 64+36=100\mapsto 1.}

8883 = 700227072 is the smallestcube in which each digit occurs exactly three times,[21] and the only cube in which three distinct digits each occur three times.[22]

Symbolism and numerology

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The number 888 is often symbolised within the international labour movement to symbolise the 8-hour day. Workers protested for 8 hours work, 8 hours rest and 8 hours time to themselves.

In someChristiannumerology, the number 888 –Eight hundred eighty-eight representsJesus. This representation may be justified either throughgematria, by counting the letter values of theGreek transliteration of Jesus' name,[23]as an opposing value to666, thenumber of the beast[24] and/or 888, as the Triple 8 means “new beginnings”. The numerological representation of Jesus with the number 888, as the sum of the numerical values of the letters of his name, was condemned by the Church fatherIrenaeus as convoluted and an act which reduced "the Lord of all things" to something alphabetical.[25]

InChinese numerology, 888 usually means triple fortune, due to 8 (pinyin: bā) sounds like 發(pinyin: fā) of 發達 (prosperity), and triplet of it is a form of strengthening of the digit 8. On its own, the number 8 is often associated with great fortune, wealth and spiritual enlightenment. Hence, 888 is considered triple.[26] For this reason, addresses and phone numbers containing the digit sequence 888 are considered particularly lucky, and may command a premium because of it.[27]

See also

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Notes

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  1. ^203 is a number whose average of divisors is60, the smallest number with twelve divisors and forty-secondcomposite.[10] On the other hand, itsaliquot sum is37,[11] and itssum-of-divisors is240,[12] which is in equivalence with the number ofroot vectors of E8 in the eighth dimension.[13] ItsEuler totient is168,[14] which is the symmetry order of theautomorphism of theFano plane in three dimensions,[15] and the product of the first twoperfect numbers.[16]
    On the other hand,1804 is a numberk such thatk64 + 1 is prime.[17]

References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A010785 (Repdigit numbers, or numbers with repeated digits)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^Nombres pratiquesArchived 2012-11-13 at theWayback Machine (in French), Jeux et Mathématiques, Jean-Paul Davalan, retrieved 2013-01-31.
  3. ^Sloane, N. J. A. (ed.)."Sequence A007850 (Giuga numbers: composite numbers n such that p divides n/p - 1 for every prime divisor p of n.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-09-20.
  4. ^Sloane, N. J. A. (ed.)."Sequence A000269 (Number of trees with n nodes, 3 of which are labeled)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^Sloane, N. J. A. (ed.)."Sequence A002494 (Number of n-node graphs without isolated nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^Sloane, N. J. A. (ed.)."Sequence A051763 (Number of nonalternating knots with n crossings)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^abSloane, N. J. A. (ed.)."Sequence A022264 (a(n) equal to n*(7*n - 1)/2.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-31.
  8. ^Tavares, Leo.Sloane, N. J. A. (ed.)."Illustration: Crysta-gons".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-31.
  9. ^Sloane, N. J. A. (ed.)."Sequence A272388 (Longest side of Heronian tetrahedron.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-09.
  10. ^Sloane, N. J. A. (ed.)."Sequence A000040 (The composite numbers.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-09.
  11. ^Sloane, N. J. A. (ed.)."Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-09.
  12. ^Sloane, N. J. A. (ed.)."Sequence A000203 (a(n) is sigma(n), the sum of the divisors of n. Also called sigma_1(n).)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-09.
  13. ^Wilson, R.A. (April 2012)."An eightfold path to E8"(PDF) (Paper).Queen Mary University London. p. 8–10.S2CID 226997354
  14. ^Sloane, N. J. A. (ed.)."Sequence A000010 (Euler totient function phi(n): count numbers less than or equal to n and prime to n.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-09.
  15. ^Lloyd, E. Keith (1995). "The Reaction Graph of the Fano Plane". In Ku, Tung-Hsin (ed.).Combinatorics and Graph Theory '95. Proceedings of the Summer School and International Conference on Combinatorics. Singapore:World Scientific. pp. 260–262.doi:10.1142/9789814532495.ISBN 978-9810223175.MR 1476206.
  16. ^Sloane, N. J. A. (ed.)."Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-09.
  17. ^Sloane, N. J. A. (ed.)."Sequence A006316 (Numbers k such that k^64 + 1 is prime.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-09.
  18. ^Sloane, N. J. A. (ed.)."Sequence A272390 (Longest side of primitive Heronian tetrahedron with 4 congruent triangle faces.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2024-03-09.
  19. ^Sloane, N. J. A. (ed.)."Sequence A051004 (Numbers divisible both by their individual digits and by the sum of their digits)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^Sloane, N. J. A. (ed.)."Sequence A002998 (Smallest multiple of n whose digits sum to n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^Sloane, N. J. A. (ed.)."Sequence A052071 (a(n)^3 is the smallest cube whose digits occur with the same frequency n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^Khovanova, Tanya (2008),Number Gossip(PDF), Gathering for Gardner,arXiv:0804.2277,Bibcode:2008arXiv0804.2277K, archived fromthe original(PDF) on 2017-12-09, retrieved2018-05-23.
  23. ^Dudley, Underwood (1997),Numerology: Or What Pythagoras Wrought,MAA Spectrum, Cambridge University Press, p. 105,ISBN 9780883855249.
  24. ^Cheiro (2005),Book Of Fate And Fortune: Numerology And Astrology, Orient Paperbacks, p. 60,ISBN 9788122200461.
  25. ^Juan Acevedo, Alphanumeric Cosmology from Greek to Arabic, Mohr Siebeck 2020 p. 159
  26. ^Ratzan, Lee (2004),Understanding Information Systems: What They Do and Why We Need Them, American Library Association, p. 202,ISBN 9780838908686.
  27. ^Hooker, John (2003),Working Across Cultures, Stanford University Press, p. 191,ISBN 9780804748070.
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