# 28 (number)

For the card game, see Twenty-eight (card game).
 ← 27 28 29 →
Cardinal twenty-eight
Ordinal 28th
(twenty-eighth)
Factorization 22× 7
Divisors 1, 2, 4, 7, 14, 28
Roman numeral XXVIII
Binary 111002
Ternary 10013
Quaternary 1304
Quinary 1035
Senary 446
Octal 348
Duodecimal 2412
Vigesimal 1820
Base 36 S36

28 (twenty-eight) is the natural number following 27 and preceding 29.

## In mathematics

7. triangular number

It is a composite number, its proper divisors being 1, 2, 4, 7, and 14.

Twenty-eight is the second perfect number. As a perfect number, it is related to the Mersenne prime 7, since 2(3 − 1)(23 − 1) = 28. The next perfect number is 496, the previous being 6.[1]

Twenty-eight is the third Granville number. The next Granville number is 96, the previous being 24.

Twenty-eight is the sum of the totient function for the first nine integers.[2]

Twenty-eight is not the aliquot sum of any number other than itself and is therefore not a component in an aliquot sequence.

Since the greatest prime factor of 282 + 1 = 785 is 157, which is more than 28 twice, 28 is a Størmer number.[3]

Twenty-eight is a harmonic divisor number,[4] a happy number,[5] a triangular number,[6] a hexagonal number,[7] and a centered nonagonal number.[8]

It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).[9]

It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 2, 8, 10, 18, 28...[10]

Twenty-eight is the third positive integer with a prime factorization of the form 22q where q is an odd prime.

Twenty-eight is the ninth and last number in early Indian magic square of order 3.

There are twenty-eight convex uniform honeycombs.

Twenty-eight is the only positive integer that has a unique Kayles nim-value.

Twenty-eight is the only known number which can be expressed as a sum of the first non negative integers (1 + 2 + 3 + 4 + 5 + 6 + 7), a sum of the first primes (2 + 3 + 5 + 7 + 11) and a sum of the first non primes (1 + 4 + 6 + 8 + 9) and there is probably no other number with this property.[11]

There are 28 oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere.[citation needed]

## In other fields

Twenty-eight is:

• An abbreviation for such years as 1928 and 2028.
• In Hebrew Gematria, koakh meaning "power", "energy" is a word that corresponds to the number 28.
• The number of Hebrew letters in Genesis 1:1, the first verse of the Bible.
• The number of wheels on a Lockheed C-5 Galaxy.
• In the code for international direct dial phone calls, +28 is unassigned.
• 028 is the ISO 3166-1 numeric 3 digit country code for Antigua and Barbuda.
• The number of days in the shortest month of the Gregorian calendar, February (except in leap years, when there are twenty-nine). All twelve months of the Gregorian calendar have at least 28 days, regardless of the year.
• The Gregorian calendar follows a 28-year cycle for the most part, since there are seven days in a week and leap year generally occurs every four years; usually, a calendar from any year is the same as that from 28 years earlier (e.g., 2008 and 1980 or 2009 and 2037). However, that rule holds only when there have been exactly seven leap days in a 28-year interval; years divisible by 100 but not by 400 are common years. Indeed, 1900 (as well as 2100, 2200, etc.) does not use the same calendar as 1872 (2072, 2172, etc., respectively) for the simple reason that 1900 is a common year. In 28 years, any day-of-the-week and date combination occurs exactly four times. February 29 will fall on each day of the week once.
• In Jewish tradition there is a 28-year solar cycle in which the sun returns to its place in Creation every 28 solar years. This is commemorated in April every 28 years with the recitation of Birkat Hachama, the blessing of the sun.
• The common name for the parrot Barnardius zonarius semitorquatus, widely distributed in Western Australia and South Australia. Its call sounds like "wenniate".
• The number of letters in the Danish and Swedish alphabets (not counting W), and also in the Arabic and Esperanto alphabets.
• In neo-Nazi circles, twenty-eight indicates Blood and Honour (28 = BH - B - second letter of the alphabet and H - the eight letter).
• The number of Chinese constellations, "Xiu" or "mansions" (a literal translation), equivalent to the 12 western zodiac constellations.
• The number of dominoes in standard domino sets.
• Deriving from the 29.46 year period of Saturn's revolution around the Sun, the 28-year cycle as well as its subdivisions by 14 and 7 are supposed in Astrology to mark significant turning points or sections in the course of a persons development in life. Thus, the number 28 has special significance in the culture of religious sects such as the Kadiri and the Mevlevi dervishes. The 28-beat metric pattern often used in the music compositions accompanying the main part of the Mevlevi sema ritual is called the "Devri kebir", meaning the "Big Circle" and is a reference to above astronomical facts about the year and the Saturn year.
• In Quebec, François Pérusse, in one of his best-selling Album du peuple made a parody of Wheel of Fortune in which all of the letters picked by the contestant were present 28 times. As a result, 28 became an almost Mythical number used by many Quebec youths, the phrase "Y'en a 28" (There are 28 [Letters]) became a running gag still used and recognized more than 15 years later.
• The Preludes, Opus 28 consists of Frédéric Chopin's 24 preludes for piano, ordinarily but not necessarily played together in concert.
• The postal code of the province of Madrid, in Spain.
• Twenty Eight is a popular game played in Kerala, India.
• The number of the French department Eure-et-Loir.
• Approximately the number of grams in an ounce, and used as such in the illegal drug trade.
• The UIC Country Code for Georgia identifying member countries of the International Union of Railways (UIC).
• The letter Q when encoding the serial number for intermodal (shipping) containers as defined by ISO 6346.
• The name of a single on the Trilogy by The Weeknd.
• The number of Panfilov's Guardsmen, said to have heroically fallen in combat on 16 November 1941 during the Battle of Moscow, and venerated as Soviet's national heroes.

## References

1. ^ "Sloane's A000396 : Perfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
2. ^ "Sloane's A002088 : Sum of totient function". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
3. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
4. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
5. ^ "Sloane's A007770 : Happy numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
6. ^ "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
7. ^ "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
8. ^ "Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
9. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
10. ^ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
11. ^ http://mathoverflow.net/questions/212985
12. ^