180 (number)
Encyclopedia
180 is the natural number
following 179
and preceding 181
.
, a positive integer with more divisors than any smaller positive integer. One of the consequences of 180 having so many divisors is that it is a practical number
, meaning that any positive number smaller than 180 that is not a divisor of 180 can be expressed as the sum of some of 180's divisors.
180 is the sum
of two square number
s: 122 + 62. It can be expressed as either the sum of six consecutive primes: 19
+ 23
+ 29
+ 31
+ 37
+ 41
, or the sum of eight consecutive primes: 11
+ 13
+ 17
+ 19
+ 23
+ 29
+ 31
+ 37
. 180 is an Ulam number
, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3.
180 is a 61-gonal
number.
Half a circle
has 180 degrees.
Summing Euler's totient function
φ(x) over the first + 24
integers gives 180.
180 is a Harshad number
in base 10, and in binary
it is a digitally balanced number, since its binary representation has the same number of zeros as ones (10110100).
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 179
179 (number)
179 is the natural number following 178 and preceding 180.-In mathematics:* 179 is an odd number* 179 is a deficient number, as 1 is less than 179* 179 is a Gaussian number* 179 is an odious number* 179 is a square-free number...
and preceding 181
181 (number)
181 is the natural number between 180 and 182.-In mathematics:* 181 is an odd number* 181 is a centered number** 181 is a centered pentagonal number** 181 is a centered 12-gonal number** 181 is a centered 18-gonal number...
.
| Cardinal Cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite... |
One hundred [and] eighty |
| Ordinal Ordinal number In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals... |
180th |
| Factorization Factorization In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original... |
 |
| Divisors | 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 |
| Roman numeral | CLXXX |
| Binary Binary numeral system The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2... |
10110100 |
| Duodecimal Duodecimal The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'... |
130 |
| Hexadecimal Hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F to represent values ten to fifteen... |
B4 |
| Vigesimal Vigesimal The vigesimal or base 20 numeral system is based on twenty .- Places :... |
90 |
In mathematics
180 is an abundant number, with its proper divisors summing up to 366. 180 is also 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....
, a positive integer with more divisors than any smaller positive integer. One of the consequences of 180 having so many divisors is that it is a practical number
Practical number
In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n...
, meaning that any positive number smaller than 180 that is not a divisor of 180 can be expressed as the sum of some of 180's divisors.
180 is the sum
Summation
Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed may be integers, rational numbers,...
of two square number
Square number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...
s: 122 + 62. It can be expressed as either the sum of six consecutive primes: 19
19 (number)
19 is the natural number following 18 and preceding 20. It is a prime number.In English speech, the numbers 19 and 90 are often confused. When carefully enunciated, they differ in which syllable is stressed: 19 vs 90...
+ 23
23 (number)
23 is the natural number following 22 and preceding 24.- In mathematics :Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. Twenty-three is also the fifth factorial prime, the third Woodall prime...
+ 29
29 (number)
29 is the natural number following 28 and preceding 30.-In mathematics:It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. It is also the sum of three...
+ 31
31 (number)
31 is the natural number following 30 and preceding 32.- In mathematics :Thirty-one is the third Mersenne prime as well as the fourth primorial prime, and together with twenty-nine, another primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496,...
+ 37
37 (number)
37 is the natural number following 36 and preceding 38.-In mathematics:It is a prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form...
+ 41
41 (number)
41 is the natural number following 40 and preceding 42.-In mathematics:Forty-one is the 13th smallest prime number. The next is forty-three, with which it comprises a twin prime...
, or the sum of eight consecutive primes: 11
11 (number)
11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name...
+ 13
13 (number)
13 is the natural number after 12 and before 14. It is the smallest number with eight letters in its name spelled out in English. It is also the first of the teens – the numbers 13 through 19 – the ages of teenagers....
+ 17
17 (number)
17 is the natural number following 16 and preceding 18. It is prime.In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 vs 70...
+ 19
19 (number)
19 is the natural number following 18 and preceding 20. It is a prime number.In English speech, the numbers 19 and 90 are often confused. When carefully enunciated, they differ in which syllable is stressed: 19 vs 90...
+ 23
23 (number)
23 is the natural number following 22 and preceding 24.- In mathematics :Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. Twenty-three is also the fifth factorial prime, the third Woodall prime...
+ 29
29 (number)
29 is the natural number following 28 and preceding 30.-In mathematics:It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. It is also the sum of three...
+ 31
31 (number)
31 is the natural number following 30 and preceding 32.- In mathematics :Thirty-one is the third Mersenne prime as well as the fourth primorial prime, and together with twenty-nine, another primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496,...
+ 37
37 (number)
37 is the natural number following 36 and preceding 38.-In mathematics:It is a prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form...
. 180 is an Ulam number
Ulam numbers
An Ulam number is a member of an integer sequence devised by and named after Stanislaw Ulam, who introduced it in 1964. The standard Ulam sequence starts with U1 = 1 and U2 = 2...
, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3.
180 is a 61-gonal
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 :...
number.
Half a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
has 180 degrees.
Summing 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 + 24
24 (number)
24 is the natural number following 23 and preceding 25.The SI prefix for 1024 is yotta , and for 10−24 yocto...
integers gives 180.
180 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, and in binary
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
it is a digitally balanced number, since its binary representation has the same number of zeros as ones (10110100).
In sports
- A "180" is a trick in extreme sports where a rider rotates half a turn while airborne and lands.
- The maximum possible score in one turn at dartsDartsDarts is a form of throwing game where darts are thrown at a circular target fixed to a wall. Though various boards and games have been used in the past, the term "darts" usually now refers to a standardised game involving a specific board design and set of rules...
(three triple 20s). - In archeryArcheryArchery is the art, practice, or skill of propelling arrows with the use of a bow, from Latin arcus. Archery has historically been used for hunting and combat; in modern times, however, its main use is that of a recreational activity...
the gent's cloutClout archeryClout is a form of archery in which archers shoot arrows at a flag from a relatively long distance and score points depending on how close each arrow lands to the flag....
shooting distance is 180 yards.
In other fields
180 is also:- The year AD 180180Year 180 was a leap year starting on Friday of the Julian calendar. At the time, it was known as the Year of the Consulship of Rusticus and Condianus...
or 180 BC180 BCYear 180 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Luscus and Piso/Flaccus... - 180 is an astrologicalAstrologyAstrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
aspect considered to be negative in influence. - Scores on the Law School Admission TestLaw School Admission TestThe Law School Admission Test is a half-day standardized test administered four times each year at designated testing centers throughout the world. Administered by the Law School Admission Council for prospective law school candidates, the LSAT is designed to assess Reading Comprehension,...
(LSAT) are converted to a scaled score from 120 - 180. - Lithol Rubine BKLithol Rubine BKLithol Rubine BK is a reddish synthetic azo dye. It has the appearance of a red powder. It is slightly soluble in hot water, insoluble in cold water, and insoluble in ethanol. When dissolved in dimethylformamide, its absorption maximum lies at about 442 nm. It usually comes as a calcium salt.It is...
, food dye classification #EE numberE numbers are number codes for food additives that have been assessed for use within the European Union . They are commonly found on food labels throughout the European Union. Safety assessment and approval are the responsibility of the European Food Safety Authority...
180 - John WayneJohn WayneMarion Mitchell Morrison , better known by his stage name John Wayne, was an American film actor, director and producer. He epitomized rugged masculinity and became an enduring American icon. He is famous for his distinctive calm voice, walk, and height...
, an American film actor, starred in 180 films. - In the Final Destination seriesFinal Destination seriesThe Final Destination series is a series of horror films based on an unproduced script written by Jeffrey Reddick for the X-Files television series. Distributed by New Line Cinema, all five films are centered on the themes of fatalism, predestination, and precognition, in relation to death...
, the number 180 is a sign of death.
See also
- List of highways numbered 180
- United Nations Security Council Resolution 180United Nations Security Council Resolution 180United Nations Security Council Resolution 180, adopted on July 31, 1963, affirmed that Portugal claiming its overseas territories as part of metropolitan Portugal was contrary to the principles of the Charter...
- United States Supreme Court cases, Volume 180
- Pennsylvania House of Representatives, District 180Pennsylvania House of Representatives, District 180The 180th Pennsylvania House of Representatives District is located in Philadelphia County and includes the following areas:* Philadelphia **Ward 07,**Ward 19 [PART, Divisions 02, 03, 04, 06, 07, 09, 10, 11, 13, 14, 15, 16, 17, 18 and 19],...
- United States v. Gouveia, 467 U.S. 180 (1984)United States v. GouveiaUnited States v. Gouveia, 467 U.S. 180 , was a case in which the United States Supreme Court held that prisoners in administrative segregation pending the investigation of crimes committed within the prison had no Sixth Amendment entitlement to counsel prior to the initiation of adversary judicial...