240 (number)
Encyclopedia
240 is the natural number
following 239
and preceding 241
.
, and it is also a refactorable number
or tau number, since it has 20 divisors and 20 divides 240. And since it has 31 totient answers, more than any previous integer, 240 is a highly totient number
.
240 is a semiperfect number
.
240 can be expressed as a sum of consecutive primes in two different ways: 240 = 53 + 59 + 61 + 67 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43. It can also be expressed as the product of two consecutive integers, 15 and 16, thus 240 is a pronic number
.
Also, being divisible by the sum of its digits, 240 is a Harshad number
, and not only that, it is also a concatenation of two of its proper divisors (see Sloane's A50480).
E8
has 240 roots.
There are 240 distinct solutions of the Soma cube
puzzle.
Two hundred [and] forty-one
has its own article.
----
Two hundred [and] forty-two
has its own article.
----
Two hundred [and] forty-three
has its own article.
----
Two hundred [and] forty-four 244 = 22·61, nontotient, noncototient, self number
.
----
Two hundred [and] forty-five
has its own article.
----
Two hundred [and] forty-six 246 = 2·3·41, sphenic number
, nontotient
, untouchable number
.
----
Two hundred [and] forty-seven 247 = 13·19, pentagonal number
.
247 = 50123 - 49876, and is the smallest number which can be expressed as the difference between two integers such that together, they contain all digits 0-9.
Sometimes (when it is a URL, etc.) may use "247" as an alternate to 24/7
, it is an abbreviation which stands for "24 hours a day, 7 days a week".
----
Two hundred [and] forty-eight 248 = 23·31, nontotient, untouchable number, refactorable number; E8
has complex dimension
248. The number 248 is also the Gematria
value for the Hebrew letters Ramach (Resh Mem and Het), traditionally depicted as the number of organs in the human body, and the number of positive commandments
in the Torah.
----
Two hundred [and] forty-nine 249 = 3·83, Blum integer
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 239
239 (number)
239 is the natural number following 238 and preceding 240.-In mathematics:It is a prime number. The next is 241, with which it forms a pair of twin primes. 239 is a Sophie Germain prime and a Newman–Shanks–Williams prime...
and preceding 241
241 (number)
241 is the natural number between 240 and 242. It is also a prime number.-In mathematics:241 is the larger of the twin primes . Prime twins are always of the form , with n = 1, 2, 3, ......
.
| 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... |
two hundred [and] forty |
| 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... |
two hundred [and] fortieth |
| 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... |  |
| Roman numeral | CCXL |
| 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... |
11110000 |
| 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... |
F0 |
In mathematics
With 20 divisors total (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240), more than any previous number, 240 is 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....
, and it is also a refactorable number
Refactorable number
A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that \tau|n. The first few refactorable numbers are listed in 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96...
or tau number, since it has 20 divisors and 20 divides 240. And since it has 31 totient answers, more than any previous integer, 240 is 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...
.
240 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....
.
240 can be expressed as a sum of consecutive primes in two different ways: 240 = 53 + 59 + 61 + 67 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43. It can also be expressed as the product of two consecutive integers, 15 and 16, thus 240 is a pronic number
Pronic number
A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n . The n-th pronic number is twice the n-th triangular number and n more than the n-th square number...
.
Also, being divisible by the sum of its digits, 240 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...
, and not only that, it is also a concatenation of two of its proper divisors (see Sloane's A50480).
E8
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8...
has 240 roots.
There are 240 distinct solutions of the Soma cube
Soma cube
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube...
puzzle.
In other fields
240 is:- A common voltageVoltageVoltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
in EnglandEnglandEngland is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
and AustraliaAustraliaAustralia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
before conversion to 230V standard. - In British currency, the number of pence in a poundPound sterlingThe pound sterling , commonly called the pound, is the official currency of the United Kingdom, its Crown Dependencies and the British Overseas Territories of South Georgia and the South Sandwich Islands, British Antarctic Territory and Tristan da Cunha. It is subdivided into 100 pence...
until 1971. - A cholesterolCholesterolCholesterol is a complex isoprenoid. Specifically, it is a waxy steroid of fat that is produced in the liver or intestines. It is used to produce hormones and cell membranes and is transported in the blood plasma of all mammals. It is an essential structural component of mammalian cell membranes...
level of 240 and above is considered high risk. - The model number of the Convair 240Convair 240The Convair CV-240 was an American airliner produced by Convair from 1947 to 1954, initially as a possible replacement of the ubiquitous Douglas DC-3. While featuring a more modern design, the 240 series was able to make some inroads as a commercial airliner and also had a long development cycle...
. - The year A.D. 240240Year 240 was a leap year starting on Wednesday of the Julian calendar. At the time, it was known as the Year of the Consulship of Sabinus and Venustus...
or 240 BC240 BCYear 240 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Centho and Tuditanus...
. - Datsun 240Z
- Mercedes 240D
- Nissan 240SXNissan 240SXThe 240SX is a two-door compact car that was introduced to the North American market by Nissan in 1988 for the following model year. It replaced the outgoing 200SX model. Most of the 240SX were equipped with the 2.4-liter inline 4 engine . The KA24E being single over-head cam and KA24DE being dual...
- Volvo 240
- An area code overlay of the 301 area code in western MarylandMarylandMaryland is a U.S. state located in the Mid Atlantic region of the United States, bordering Virginia, West Virginia, and the District of Columbia to its south and west; Pennsylvania to its north; and Delaware to its east...
. - The famous skit by the sketch comedy group The StateThe State (TV series)The State is a half-hour sketch-comedy television show, originally broadcast on MTV between December 17, 1993 and July 1, 1995. The show combined bizarre characters and scenarios to present sketches that won the favor of its target teenaged audience...
is entitled "$240 Dollars Worth of Pudding"
241 - 249
----Two hundred [and] forty-one
241 (number)
241 is the natural number between 240 and 242. It is also a prime number.-In mathematics:241 is the larger of the twin primes . Prime twins are always of the form , with n = 1, 2, 3, ......
has its own article.
----
Two hundred [and] forty-two
242 (number)
242 is the natural number following 241 and preceding 243.-In mathematics:242 is the smallest integer to start a run of four consecutive integers with the same number of divisors.242 is a nontotient since there is no integer with 242 coprimes below it....
has its own article.
----
Two hundred [and] forty-three
243 (number)
243 is the natural number following 242 and preceding 244.-In mathematics:243 is:*the largest 3-digit number that is a fifth power .*a perfect totient number....
has its own article.
----
Two hundred [and] forty-four 244 = 22·61, nontotient, noncototient, self number
Self number
A self number, Colombian number or Devlali number is an integer which, in a given base, cannot be generated by any other integer added to the sum of that other integer's digits. For example, 21 is not a self number, since it can be generated by the sum of 15 and the digits comprising 15, that is,...
.
----
Two hundred [and] forty-five
245 (number)
245 is the natural number following 244 and preceding 246.-245 in online public access catalogs:Two hundred forty-five 245 = 5·72. In the MARC format for records in online public access catalogs, in which each type of information about a book is identified with a 3-digit number, 245 identifies...
has its own article.
----
Two hundred [and] forty-six 246 = 2·3·41, sphenic number
Sphenic number
In number theory, a sphenic number is a positive integer which is the product of three distinct prime numbers.Note that this definition is more stringent than simply requiring the integer to have exactly three prime factors; e.g. 60 = 22 × 3 × 5 has exactly 3 prime factors, but is not sphenic.All...
, nontotient
Nontotient
In number theory, a nontotient is a positive integer n which is not in the range of Euler's totient function φ, that is, for which φ = n has no solution. In other words, n is a nontotient if there is no integer x that has exactly n coprimes below it. All odd numbers are nontotients, except 1,...
, 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 ....
.
----
Two hundred [and] forty-seven 247 = 13·19, pentagonal number
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical...
.
247 = 50123 - 49876, and is the smallest number which can be expressed as the difference between two integers such that together, they contain all digits 0-9.
Sometimes (when it is a URL, etc.) may use "247" as an alternate to 24/7
24/7
24/7 is an abbreviation which stands for "24 hours a day, 7 days a week", usually referring to a business or service available at all times without interruption...
, it is an abbreviation which stands for "24 hours a day, 7 days a week".
----
Two hundred [and] forty-eight 248 = 23·31, nontotient, untouchable number, refactorable number; E8
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8...
has complex dimension
Complex dimension
In mathematics, complex dimension usually refers to the dimension of a complex manifold M, or complex algebraic variety V. If the complex dimension is d, the real dimension will be 2d...
248. The number 248 is also the Gematria
Gematria
Gematria or gimatria is a system of assigning numerical value to a word or phrase, in the belief that words or phrases with identical numerical values bear some relation to each other, or bear some relation to the number itself as it may apply to a person's age, the calendar year, or the like...
value for the Hebrew letters Ramach (Resh Mem and Het), traditionally depicted as the number of organs in the human body, and the number of positive commandments
Mitzvah
The primary meaning of the Hebrew word refers to precepts and commandments as commanded by God...
in the Torah.
----
Two hundred [and] forty-nine 249 = 3·83, Blum integer
Blum integer
In mathematics, a natural number n is a Blum integer if n = p×q is a semiprime for which p and q are distinct prime numbers congruent to 3 mod 4. That is, p and q must be of the form 4t+3, for some integer t. Primes of this form are referred to as Blum primes. This means that the factors of a Blum...