.gif)
78 (number)
Encyclopedia
78 is the natural number
following 77
and followed by 79
.
, and its factorization
makes it a sphenic number
. As a multiple of a perfect number, 78 is itself a semiperfect number
.
77 and 78 form a Ruth-Aaron pair
under the second definition in which repeated prime factors are counted as often as they occur.
Since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member, 78 is an Erdős–Woods number
.
Karl A. Dahlke proved in 1989 that 78 heptomino
s of this shape (
), at a minimum, are required to fill a rectangle.
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 77
77 (number)
77 is the natural number following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English.-In mathematics:...
and followed by 79
79 (number)
Seventy-nine is the natural number following 78 and preceding 80.79 may represent:-In mathematics:*An odd number*The smallest number that can't be represented as a sum of fewer than 19 fourth powers*A strictly non-palindromic number...
.
In mathematics
78 is a triangular numberTriangular 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...
, and its 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...
makes it a 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...
. As a multiple of a perfect number, 78 is itself 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....
.
77 and 78 form a Ruth-Aaron pair
Ruth-Aaron pair
In mathematics, a Ruth–Aaron pair consists of two consecutive integers for which the sums of the prime factors of each integer are equal:andIf only distinct prime factors are counted, the first few Ruth–Aaron pairs are:...
under the second definition in which repeated prime factors are counted as often as they occur.
Since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member, 78 is an Erdős–Woods number
Erdos–Woods number
In number theory, an Erdős–Woods number is a positive integer that has the following property:Consider a sequence of consecutive positive integers [a, a+1, \dots, a+k]. The number k is an Erdős–Woods number if there exists such a sequence, beginning with some number a, in which each of the elements...
.
Karl A. Dahlke proved in 1989 that 78 heptomino
Polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling with a connected interior....
s of this shape (
), at a minimum, are required to fill a rectangle.In other fields
78 is also:- In reference to gramophone recordGramophone recordA gramophone record, commonly known as a phonograph record , vinyl record , or colloquially, a record, is an analog sound storage medium consisting of a flat disc with an inscribed, modulated spiral groove...
s, 78 refers those meant to be spun at 78 revolutions per minuteRevolutions per minuteRevolutions per minute is a measure of the frequency of a rotation. It annotates the number of full rotations completed in one minute around a fixed axis...
. Compare: LPGramophone recordA gramophone record, commonly known as a phonograph record , vinyl record , or colloquially, a record, is an analog sound storage medium consisting of a flat disc with an inscribed, modulated spiral groove...
, 33 1/3 and 45 rpm. 33+45=78 - A typical tarotTarotThe tarot |trionfi]] and later as tarocchi, tarock, and others) is a pack of cards , used from the mid-15th century in various parts of Europe to play a group of card games such as Italian tarocchini and French tarot...
deck containing the 21 trump cards, the FoolThe Fool (Tarot card)The Fool or The Jester is one of the 78 cards in a Tarot deck; one of the 22 Trump cards that make up the Major Arcana. The Fool is unnumbered...
and the 56 suit cards make up 78 cards - The total number of gifts in the song The Twelve Days of Christmas (since 78 is the 12th triangular number)
- The number of lines that make up Metatron's CubeMetatron's CubeMetatron's Cube is a two-dimensional geometric figure created from 13 equal circles with lines from the center of each circle extending out to the centers of the other 12 circles. Six circles are placed in a hexagonal pattern around a central circle, with six more extending out along the same...
- The Rule of 78sRule of 78sAlso known as the sum-of-the-digits method, the Rule of 78s is a term used in lending that refers to a method of yearly interest calculation. The name comes from the total number of months' interest that is being calculated in a year...
is a method of yearly interest calculation - Municipal Okrug 78, a municipal okrug of Tsentralny District of St. Petersburg, Russia