120 (one hundred ndtwenty) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 119 and preceding 121. In the

Germanic languages The Germanic languages are a branch of the Indo-European languages, Indo-European language family spoken natively by a population of about 515 million people mainly in Europe, North America, Oceania, and Southern Africa. The most widely spoke ...

, the number 120 was also formerly known as "one hundred". This "hundred" of six score is now obsolete but is described as the long hundred or great hundred in historical contexts.

In mathematics

120 is * the

factorial In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times ...

of 5, i.e.,

5!=5\cdot 4\cdot 3\cdot 2\cdot 1

. * the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a

tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular ...

. 120 is the smallest number to appear six times in

Pascal's triangle In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Bla ...

(as all triangular and tetragonal numbers appear in it). Because 15 is also triangular, 120 is a doubly triangular number. 120 is divisible by the first five triangular numbers and the first four tetrahedral numbers. It is the eighth hexagonal number. * The 10th highly composite, the 5th superior highly composite, superabundant, and the 5th colossally abundant number. It is also a sparsely totient number. 120 is also the smallest highly composite number with no adjacent prime number, being adjacent to

119=7\cdot 17

and

121=11^2.

It is also the smallest positive multiple of six not adjacent to a prime. * 120 is the first multiply perfect number of order three (''a 3-perfect'' or '' triperfect number''). The sum of its factors (including one and itself) sum to

360 360 may refer to: * 360 (number) * 360 AD, a year * 360 BC, a year * 360 degrees, a turn Businesses and organizations * 360 Architecture, an American architectural design firm * Ngong Ping 360, a tourism project in Lantau Island, Hong Kong ...

, exactly three times 120.

Perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfec ...

s are order two (''2-perfect'') by the same definition. * 120 is the sum of a

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...

pair (59 + 61) and the sum of four consecutive

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

s (23 + 29 + 31 + 37), four consecutive

powers of two A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^n(1). In the Hardy hi ...

(8 + 16 + 32 + 64), and four consecutive powers of three (3 + 9 + 27 + 81). *120 is divisible by the number of primes below it (30). However, there is no integer that has 120 as the sum of its proper divisors, making 120 an untouchable number. * The sum of

Euler's totient function In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In ot ...

\phi (x)

over the first nineteen integers is 120. * As 120 is a factorial and one less than a square (

5!=11^-1

), it—with 11—is one of the few Brown number pairs. *120 appears in

Pierre de Fermat Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his d ...

's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that, when multiplied by any of the other numbers in the sequence, yields a number that is one less than a square.

Leonhard Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

also searched for this number. He failed to find an integer, but he did find a fraction that meets the other conditions:

\frac

. *The internal angles of a regular hexagon (one where all sides and angles are equal) are all 120 degrees.

In science

In electrical engineering, each line of the three-phase system are 120 degrees apart from each other. Three soap films meet along a Plateau border at 120° angles.

In religion

* The age at which

Moses In Abrahamic religions, Moses was the Hebrews, Hebrew prophet who led the Israelites out of slavery in the The Exodus, Exodus from ancient Egypt, Egypt. He is considered the most important Prophets in Judaism, prophet in Judaism and Samaritani ...

died (Deut. 34:7). ** By extension, in Jewish tradition, to wish someone a long life, one says, " Live until 120". * In

astrology Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...

, 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 to the person's life.

In other fields

120 is also: * TT scale, a scale for model trains, is 1:120. * The Standard AC Voltage in US,

Canada Canada is a country in North America. Its Provinces and territories of Canada, ten provinces and three territories extend from the Atlantic Ocean to the Pacific Ocean and northward into the Arctic Ocean, making it the world's List of coun ...

Mexico Mexico, officially the United Mexican States, is a country in North America. It is the northernmost country in Latin America, and borders the United States to the north, and Guatemala and Belize to the southeast; while having maritime boundar ...

and some other countries.

References

* Wells, D. '' The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 135 {{DEFAULTSORT:120 (Number) Integers