120 (number)
Encyclopedia
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 119
119 (number)
119 is the natural number following 118 and preceding 120.- Mathematics :* 119 is a Perrin number, preceded in the sequence by 51, 68, 90 ....
and preceding 121
121 (number)
121 is the natural number following 120 and preceding 122.-In mathematics:One hundred [and] twenty-one is a square and is the sum of three consecutive primes . There are no squares besides 121 known to be of the form 1 + p + p^2 + p^3 + p^4, where p is prime...
. 120 was known as "the great hundred", especially prior to the year 1700, from the Teutonic
Germanic languages
The Germanic languages constitute a sub-branch of the Indo-European language family. The common ancestor of all of the languages in this branch is called Proto-Germanic , which was spoken in approximately the mid-1st millennium BC in Iron Age northern Europe...
Hundert which equalled 120. The number 100
100 (number)
100 is the natural number following 99 and preceding 101.-In mathematics:One hundred is the square of 10...
, now known commonly as "one hundred" was then known as "the small hundred". It is also known as 'twelvety' according to the number naming system invented by J. R. R. Tolkien
J. R. R. Tolkien
John Ronald Reuel Tolkien, CBE was an English writer, poet, philologist, and university professor, best known as the author of the classic high fantasy works The Hobbit, The Lord of the Rings, and The Silmarillion.Tolkien was Rawlinson and Bosworth Professor of Anglo-Saxon at Pembroke College,...
(c.f. eleventy
110 (number)
110 is the natural number following 109 and preceding 111.It is also known as "eleventy", a term made famous by linguist and author J. R. R...
).
In mathematics
120 is the factorialFactorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
of 5, and the sum of a twin prime
Twin prime
A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
pair (59 + 61). 120 is the sum of four consecutive prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s (23 + 29 + 31 + 37), four consecutive powers of 2 (8+16+32+64), and four consecutive powers of 3 (3 + 9 + 27 + 81). It is highly composite
Highly 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....
, superabundant, and colossally abundant number
Colossally abundant number
In mathematics, a colossally abundant number is a natural number that, in some rigorous sense, has a lot of divisors...
, with its 16 divisors being more than any number lower than it has, and it is also the smallest number to have exactly that many divisors. It is also a sparsely totient number. 120 is the smallest number to appear six times in Pascal's triangle
Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...
. 120 is also the smallest multiple of 6 with no adjacent prime number.
It is the eighth hexagonal number
Hexagonal number
A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...
and the fifteenth triangular number
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number
Tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...
. 120 is divisible by the first 5 triangular numbers and the first 4 tetrahedral numbers.
120 is the first multiply perfect number
Multiply perfect number
In mathematics, a multiply perfect number is a generalization of a perfect number....
of order three (a 3-perfect number, triperfect). The sum of its factors (including one and itself) sum to 360; exactly three times 120. Note that perfect number
Perfect number
In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself . Equivalently, a perfect number is a number that is half the sum of all of its positive divisors i.e...
s are order two (2-perfect) by the same definition.
120 is divisible by the number of primes below it, 30 in this case. However there is no integer which has 120 as the sum of its proper divisors, making 120 an untouchable number
Untouchable number
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer ....
.
The sum of Euler's totient function
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...
φ(x) over the first nineteen integers is 120.
120 figures in Pierre de Fermat
Pierre de Fermat
Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France, and an amateur mathematician who is given credit for early developments that led to infinitesimal calculus, including his adequality...
's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that multiplied with any of the other numbers in the sequence yields a number that is one less than a square. Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
also searched for this number, but failed to find it, but did find a fractional number that meets the other conditions, 777480 / 28792.
The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120 degree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
s.
120 is 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...
in base 10
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
.
In science
120 is the atomic numberAtomic number
In 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 Unbinilium
Unbinilium
Unbinilium , also called eka-radium or element 120, is the temporary, systematic element name of a hypothetical chemical element in the periodic table that has the temporary symbol Ubn and has the atomic number 120....
, an element yet to be discovered.
In astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
observers note when planets are 120 degrees apart.
In religion
- The cubitCubitThe cubit is a traditional unit of length, based on the length of the forearm. Cubits of various lengths were employed in many parts of the world in Antiquity, in the Middle Ages and into Early Modern Times....
s of the height of the Temple buildingTemple in JerusalemThe Temple in Jerusalem or Holy Temple , refers to one of a series of structures which were historically located on the Temple Mount in the Old City of Jerusalem, the current site of the Dome of the Rock. Historically, these successive temples stood at this location and functioned as the centre of...
(II ChroniclesBooks of ChroniclesThe Books of Chronicles are part of the Hebrew Bible. In the Masoretic Text, it appears as the first or last book of the Ketuvim . Chronicles largely parallels the Davidic narratives in the Books of Samuel and the Books of Kings...
3:4) - The age at which MosesMosesMoses was, according to the Hebrew Bible and Qur'an, a religious leader, lawgiver and prophet, to whom the authorship of the Torah is traditionally attributed...
died (Deut. 34:7). "Ad me'ah v'esrim shanah" (עד מאה ועשרים שנה) is a common HebrewHebrew languageHebrew is a Semitic language of the Afroasiatic language family. Culturally, is it considered by Jews and other religious groups as the language of the Jewish people, though other Jewish languages had originated among diaspora Jews, and the Hebrew language is also used by non-Jewish groups, such...
blessing for longevity - The number of Men of the Great AssemblyGreat AssemblyThe Great Assembly or Anshei Knesset HaGedolah , also known as the Great Synagogue, was, according to Jewish tradition, an assembly of 120 scribes, sages, and prophets, in the period from the end of the Biblical prophets to the time of the development of Rabbinic Judaism, marking a transition from...
who canonized the Books of 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...
and formulated the Jewish prayersJewish servicesJewish prayer are the prayer recitations that form part of the observance of Judaism. These prayers, often with instructions and commentary, are found in the siddur, the traditional Jewish prayer book.... - The number of talents of gold Queen Sheba gave to King Solomon in tribute (I KingsBooks of KingsThe Book of Kings presents a narrative history of ancient Israel and Judah from the death of David to the release of his successor Jehoiachin from imprisonment in Babylon, a period of some 400 years...
10:10) - The number of princes King Darius set over his kingdom (DanielBook of DanielThe Book of Daniel is a book in the Hebrew Bible. The book tells of how Daniel, and his Judean companions, were inducted into Babylon during Jewish exile, and how their positions elevated in the court of Nebuchadnezzar. The court tales span events that occur during the reigns of Nebuchadnezzar,...
6:2) - The weight in shekelShekelShekel , is any of several ancient units of weight or of currency. The first usage is from Mesopotamia around 3000 BC. Initially, it may have referred to a weight of barley...
s of the gold spoons offered by each tribe of Israel (Num. 7:86). - In astrologyAstrologyAstrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
, when two planets in a person's chart are 120 degrees apart from each other, this is called a trine. This is supposed to bring good luck in the person's life.
In sports
- The height in inches of a regulation basketball hoop
- In Super Mario 64Super Mario 64is a platform game, published by Nintendo and developed by its EAD division, for the Nintendo 64. Along with Pilotwings 64, it was one of the launch titles for the console. It was released in Japan on June 23, 1996, and later in North America, Europe, and Australia. Super Mario 64 has sold over...
for the Nintendo 64Nintendo 64The , often referred to as N64, was Nintendo′s third home video game console for the international market. Named for its 64-bit CPU, it was released in June 1996 in Japan, September 1996 in North America, March 1997 in Europe and Australia, September 1997 in France and December 1997 in Brazil...
120 is the maximum number of power starStarA star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s a player can get, and the max number of shine spritesSuper Mario Sunshineis a platforming video game developed by Nintendo Entertainment Analysis and Development and published by Nintendo for the Nintendo GameCube. It was released in Japan in July 2002, in North America in August 2002, and in Europe and Australia in October 2002...
in Super Mario SunshineSuper Mario Sunshineis a platforming video game developed by Nintendo Entertainment Analysis and Development and published by Nintendo for the Nintendo GameCube. It was released in Japan in July 2002, in North America in August 2002, and in Europe and Australia in October 2002... - In the NCAA, the number of Division 1-A Schools.
In other fields
120 is also:- The medicalMedicineMedicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....
telephone numberEmergency telephone numberMany countries' public telephone networks have a single emergency telephone number, sometimes known as the universal emergency telephone number or occasionally the emergency services number, that allows a caller to contact local emergency services for assistance. The emergency telephone number may...
in ChinaChinaChinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture... - In AustriaAustriaAustria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
, the telephone number "to report a car breakdown on the highway. - In the US Army, a common diameter for a mortar in mm (M120).
See also
- List of highways numbered 120
- United Nations Security Council Resolution 120United Nations Security Council Resolution 120United Nations Security Council Resolution 120, adopted on November 4, 1956, considering the grave situation created by the Union of Soviet Socialist Republics in the suppression of the Hungarian people in asserting their rights, and the lack of unanimity of its permanent members, the Council felt...