48 (number)
Encyclopedia
48 is the natural number
following 47
and preceding 49
. It is one third of a gross
or four dozen
s.
. Like all other multiples of 6, it is a semiperfect number
. 48 is the second 17-gonal number
.
48 is in abundance having an aliquot sum of 76. It is the lowest composite number
to fall into the 41-aliquot tree having the 7 aliquot number sequence,(48, 76 , 64, 63, 41, 1, 0). 48 is highly abundant with an aliquot sum 158% higher than itself.
48 is the smallest number with exactly ten divisors.
There are 11 solutions to the equation φ
(x) = 48, namely 65, 104, 105, 112, 130, 140, 144, 156, 168, 180 and 210. This is more than any integer below 48, making 48 a highly totient number
.
Since the greatest prime factor of 482 + 1 = 2305 is 461, which is clearly more than 48 twice, 48 is a Størmer number.
48 is in base 10 a Harshad number
. It has 24, 2, 12,and 4 as factors.
, 48 B.C.
, 1848
, 1948, 2048, etc.
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
following 47
47 (number)
47 is the natural number following 46 and preceding 48.-In mathematics:Forty-seven is the fifteenth prime number, a safe prime, the thirteenth supersingular prime, and the sixth Lucas prime. Forty-seven is a highly cototient number...
and preceding 49
49 (number)
49 is the natural number following 48 and preceding 50.-In mathematics:* Forty-nine is the square of seven and is therefore the fourth squared prime number.The aliquot sum of forty-nine is 8...
. It is one third of a gross
Gross (unit)
A gross is equal to a dozen dozen, i.e. 12 × 12 = 144.It can be used in duodecimal counting. The use of gross likely originated from the fact that 144 can be counted on the fingers using the fingertips and first two joints of each finger when marked by the thumb of one hand. The other hand...
or four dozen
Dozen
A dozen is a grouping of approximately twelve. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon or months in a cycle of the sun or year...
s.
In mathematics
Forty-eight is a double factorial of 6, a highly composite numberHighly composite number
A highly composite number is a positive integer with more divisors than any positive integer smaller than itself.The initial or smallest twenty-one highly composite numbers are listed in the table at right....
. Like all other multiples of 6, it is a semiperfect number
Semiperfect number
In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number....
. 48 is the second 17-gonal number
Polygonal number
In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas . These are one type of 2-dimensional figurate numbers.- Definition and examples :...
.
48 is in abundance having an aliquot sum of 76. It is the lowest composite number
Composite number
A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number....
to fall into the 41-aliquot tree having the 7 aliquot number sequence,(48, 76 , 64, 63, 41, 1, 0). 48 is highly abundant with an aliquot sum 158% higher than itself.
48 is the smallest number with exactly ten divisors.
There are 11 solutions to the equation φ
Euler's totient function
In number theory, the totient \varphi of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n In number theory, the totient \varphi(n) of a positive integer n is defined to be the number of positive integers less than or equal to n that...
(x) = 48, namely 65, 104, 105, 112, 130, 140, 144, 156, 168, 180 and 210. This is more than any integer below 48, making 48 a highly totient number
Highly totient number
A highly totient number k is an integer that has more solutions to the equation φ = k, where φ is Euler's totient function, than any integer below it. The first few highly totient numbers are...
.
Since the greatest prime factor of 482 + 1 = 2305 is 461, which is clearly more than 48 twice, 48 is a Størmer number.
48 is in base 10 a Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...
. It has 24, 2, 12,and 4 as factors.
In science
- The atomic numberAtomic numberIn chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
of cadmiumCadmiumCadmium is a chemical element with the symbol Cd and atomic number 48. This soft, bluish-white metal is chemically similar to the two other stable metals in group 12, zinc and mercury. Similar to zinc, it prefers oxidation state +2 in most of its compounds and similar to mercury it shows a low... - The number of PtolemaicPtolemyClaudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
s
Astronomy
- Messier objectMessier objectThe Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...
M48, a magnitude 5.5 open clusterOpen clusterAn open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way Galaxy, and many more are thought to exist...
in the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
HydraHydra (constellation)Hydra is the largest of the 88 modern constellations, measuring 1303 square degrees. It has a long history, having been included among the 48 constellations listed by the 2nd century astronomer Ptolemy. It is commonly represented as a water snake... - The New General CatalogueNew General CatalogueThe New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...
object NGC 48NGC 48The New General Catalogue NGC 48, a barred spiral galaxy in the constellation Andromeda.-External links:* http://www.seds.org/~spider/ngc/ngc.cgi?48* http://www.seds.org/~spider/ngc/ngc_fr.cgi?48* http://www.seds.org/~spider/ngc/revngcic.cgi?NGC48...
, a barred spiral galaxyBarred spiral galaxyA barred spiral galaxy is a spiral galaxy with a central bar-shaped structure composed of stars. Bars are found in approximately two-thirds of all spiral galaxies...
in the constellation AndromedaAndromeda (constellation)Andromeda is a constellation in the northern sky. It is named after Andromeda, the princess in the Greek legend of Perseus who was chained to a rock to be eaten by the sea monster Cetus... - The Saros number of the solar eclipseSolar eclipseAs seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
series which began on -1331 February 8 and ended on -15 April 9. The duration of Saros series 48 was 1316.2 years, and it contained 74 solar eclipses. - The Saros number of the lunar eclipseLunar eclipseA lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
series which began on -1246 July 11 and ended on 124 October. The duration of Saros series 48 was 1370.3 years, and it contained 77 lunar eclipses.
In religion
- The prophecies of 48 Jewish prophetProphetIn religion, a prophet, from the Greek word προφήτης profitis meaning "foreteller", is an individual who is claimed to have been contacted by the supernatural or the divine, and serves as an intermediary with humanity, delivering this newfound knowledge from the supernatural entity to other people...
s and 7 prophetesses http://www.askmoses.com/article.html?h=248&o=89728 were recorded in the TanakhTanakhThe Tanakh is a name used in Judaism for the canon of the Hebrew Bible. The Tanakh is also known as the Masoretic Text or the Miqra. The name is an acronym formed from the initial Hebrew letters of the Masoretic Text's three traditional subdivisions: The Torah , Nevi'im and Ketuvim —hence...
for posterity - According to the MishnahMishnahThe Mishnah or Mishna is the first major written redaction of the Jewish oral traditions called the "Oral Torah". It is also the first major work of Rabbinic Judaism. It was redacted c...
, TorahTorahTorah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five books of the bible—Genesis , Exodus , Leviticus , Numbers and Deuteronomy Torah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five...
wisdom is acquired via 48 ways (Pirkei AvothPirkei AvothPirkei Avot , which translates to English as Chapters of the Fathers is a compilation of the ethical teachings and maxims of the Rabbis of the Mishnaic period. Because of its contents, it is also called Ethics of the Fathers. The teachings of Pirkei Avot appear in the Mishnaic tractate of Avot,...
6:6) - Siddhartha Gautama, the founder of BuddhismBuddhismBuddhism is a religion and philosophy encompassing a variety of traditions, beliefs and practices, largely based on teachings attributed to Siddhartha Gautama, commonly known as the Buddha . The Buddha lived and taught in the northeastern Indian subcontinent some time between the 6th and 4th...
, sat under a bodhi tree for 48 days attempting to understand the nature of reality and Universe. Buddhism was the result.
In music
- 48 is twice the total number of major and minor keys in Western tonal music (twenty-four), not counting enharmonic equivalents. Johann Sebastian BachJohann Sebastian BachJohann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...
's Well-Tempered Clavier is informally known as The Forty-Eight because it consists of a prelude and a fugue in each major and minor key, for a total of forty-eight pieces. - 48 is a song by Sunny Day Real EstateSunny Day Real EstateSunny Day Real Estate is an American rock band from Seattle, Washington. In the 1990s, the group expanded upon the grunge style that was popular in the local scene to make a more melodic sound. While not the first band to be classified as emo, they were instrumental in establishing the genre. In...
- 48 Hour Parole is a song by the Hollies
- 48 Crash48 Crash"48 Crash" is Suzi Quatro's second single after "Can the Can". It was included on her debut album Suzi Quatro . The single peaked at number three in the U.K. in July 1973, and number one in Australia for one week...
is a song by Suzi QuatroSuzi QuatroSusan Kay "Suzi" Quatro is an American singer-songwriter, bass player, and actor.She scored a string of hit singles in the 1970s that found greater success in Europe and Australia than in her homeland, and had a recurring role on the popular American sitcom Happy Days.-Music:Quatro began her... - Formerly known as BoneheadBonehead (band)Bonehead were an American alternative rock band active in the late 1990s and early 2000s. They are best known for their US radio hit, "The Question".-History:...
, Familiar 48 is an alternative pop/rock band - The jam band PhishPhishPhish is an American rock band noted for its musical improvisation, extended jams, and exploration of music across genres. Formed at the University of Vermont in 1983 , the band's four members – Trey Anastasio , Mike Gordon , Jon Fishman , and Page McConnell Phish is an American rock band...
has 48 albums to date. - On the band tool’s album, ÆnimaÆnimaÆnima is the second studio album by American rock band Tool. The album was released on September 17, 1996 in vinyl format and on October 1, 1996 in Compact Disc format. The album was recorded and cut at Ocean Way, Hollywood, California and The Hook, North Hollywood, California from 1995 to 1996...
, there is a song named Forty-Six & 2; the sum of which is 48. - AKB48AKB48AKB48 is a Japanese female idol group produced by Yasushi Akimoto.The group has achieved enormous popularity in Japan. Its ten latest consecutive singles topped the Oricon Weekly Singles Chart...
is the name of a Japanese pop idol group that consists of approximately 48 members.
In sports
- 48 is the number of a NASCAR car owned by Hendrick MotorsportsHendrick MotorsportsHendrick Motorsports , originally named All Star Racing, is a current American auto racing team created in 1984 by Rick Hendrick. The team currently competes in the NASCAR Sprint Cup Series with Chevrolet Impalas...
. It is currently being driven by 5-time and defending NASCAR Sprint Cup champion Jimmie JohnsonJimmie JohnsonJimmie Kenneth Johnson is an American NASCAR Sprint Cup Series race car driver. He currently drives the No. 48 Lowe's Chevrolet for Hendrick Motorsports....
. - 48 is the retired number of former USA President Gerald FordGerald FordGerald Rudolph "Jerry" Ford, Jr. was the 38th President of the United States, serving from 1974 to 1977, and the 40th Vice President of the United States serving from 1973 to 1974...
's jersey at the University of MichiganUniversity of MichiganThe University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
In other fields
Forty-eight may also refer to:- the code for international direct dial phone calls to PolandPolandPoland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
- the model number of the HP-48 S/SX/G/GX/G+/GII
- the 48 Hour Film Project48 Hour Film ProjectThe 48 Hour Film Project is a contest in which teams of filmmakers are assigned a genre, a character, a prop, and a line of dialogue, and have 48 hours to create a short film containing those elements. Shortly after the 48 hours of filmmaking, the films from each city are then screened at a theater...
- The First 48The First 48The First 48 is an American documentary television series that airs on A&E. Filmed in various cities in the United States, the series offers an insider's look at the real-life world of homicide investigators...
, an American crime program, 2004-present - 48 Hours48 Hours (TV series)48 Hours is a documentary and news program broadcast on the CBS television network since January 19, 1988. The program originally presented documentaries of various events related to a particular subject occurring within a 48-hour period, and is credited as one of the first to air a "reality show"...
is a television news program on CBSCBSCBS Broadcasting Inc. is a major US commercial broadcasting television network, which started as a radio network. The name is derived from the initials of the network's former name, Columbia Broadcasting System. The network is sometimes referred to as the "Eye Network" in reference to the shape of... - 48 Hrs.48 Hrs.48 Hrs. is a 1982 American action comedy film directed by Walter Hill, starring Nick Nolte and Eddie Murphy as a cop and convict, respectively, who team up to catch a cop-killer. The title refers to the amount of time they have to solve the crime. This was Eddie Murphy's film debut , and Joel...
, a 1982 film starring Nick NolteNick NolteNicholas King "Nick" Nolte is an American actor whose career has spanned over five decades, peaking in the 1990s when his commercial success made him one of the most popular celebrities of that decade.-Early life:...
and Eddie MurphyEddie MurphyEdward Regan "Eddie" Murphy is an American stand-up comedian, actor, writer, singer, director, and musician....
, followed by Another 48 Hrs.Another 48 Hrs.Another 48 Hrs. is a 1990 action-comedy film and a sequel to the 1982 film 48 Hrs.. It was directed by Walter Hill and stars Eddie Murphy, Nick Nolte, Brion James, Andrew Divoff, and Ed O'Ross. Nolte returns as San Francisco police officer Jack Cates, who has 48 hours to clear his name from a... - ArizonaArizonaArizona ; is a state located in the southwestern region of the United States. It is also part of the western United States and the mountain west. The capital and largest city is Phoenix...
is the 48th stateU.S. stateA U.S. state is any one of the 50 federated states of the United States of America that share sovereignty with the federal government. Because of this shared sovereignty, an American is a citizen both of the federal entity and of his or her state of domicile. Four states use the official title of...
in the Union - The 48 United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
(excluding Alaska and Hawaii) are also referred to as the "Lower 48" or the "48 contiguous states" - '48 is an alternate history novel by James HerbertJames HerbertJames Herbert, OBE is a best-selling English horror writer who originally worked as the art director of an advertising agency. He is a full-time writer who also designs his own book covers and publicity.-Family:...
- The 48 Laws of PowerThe 48 Laws of PowerThe 48 Laws of Power is a 1998 book by Robert Greene. Robert Greene takes elements of some of the worlds most influential political thinkers to come up with the 48 Laws of Power, from Niccolò Machiavelli to Sun Tsu, he captures their most important points of power. - The Laws :# Never outshine the...
is a book by Robert Greene - The number 48 in ASCIIASCIIThe American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text...
is what you add to any single digit integer to convert to its ASCII value - MAC addressMAC addressA Media Access Control address is a unique identifier assigned to network interfaces for communications on the physical network segment. MAC addresses are used for numerous network technologies and most IEEE 802 network technologies, including Ethernet...
uses 48-bitBitA bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
(6-byteByteThe byte is a unit of digital information in computing and telecommunications that most commonly consists of eight bits. Historically, a byte was the number of bits used to encode a single character of text in a computer and for this reason it is the basic addressable element in many computer...
) - The number of the French department LozèreLozèreLozère , is a department in southeast France near the Massif Central, named after Mont Lozère.- History :Lozère is one of the original 83 departments created during the French Revolution on March 4, 1790...
- a model of Harley-DavidsonHarley-DavidsonHarley-Davidson , often abbreviated H-D or Harley, is an American motorcycle manufacturer. Founded in Milwaukee, Wisconsin, during the first decade of the 20th century, it was one of two major American motorcycle manufacturers to survive the Great Depression...
in the Sportster line
Historical years
48 A.D.353
Year 353 was a common year starting on Friday of the Julian calendar. At the time, it was known as the Year of the Consulship of Magnentius and Decentius...
, 48 B.C.
48 BC
Year 48 BC was a year of the pre-Julian Roman calendar. At the time, it was known as the Year of the Consulship of Caesar and Vatia...
, 1848
Revolutions of 1848
The European Revolutions of 1848, known in some countries as the Spring of Nations, Springtime of the Peoples or the Year of Revolution, were a series of political upheavals throughout Europe in 1848. It was the first Europe-wide collapse of traditional authority, but within a year reactionary...
, 1948, 2048, etc.