divisibility wikipedia - EAS

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    From Wikipedia, the free encyclopedia A divisibility rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits.
    en.wikipedia.org/wiki/Divisibility_rule
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    What is the meaning of divisibility?
    divisibility (countable and uncountable, plural divisibilities) (uncountable) The state of being divisible. The state capable of being divided. (arithmetic) The property of being divisible by a particular integer.
    en.wiktionary.org/wiki/divisibility
    What is divisibility rule in ABA?
    A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. ... 75: Number must be divisible by 3 ending in 00, 25, 50 or 75. 77: Number is divisible by 7 and 11.
    en.wikipedia.org/wiki/Divisibility_rule
    What is the shorthand way of determining whether a number is divisible?
    Shorthand way of determining whether a given number is divisible by a fixed divisor. A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits.
    en.wikipedia.org/wiki/Divisibility_rule
    What is the divisibility rule for 4?
    The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4.
    en.wikipedia.org/wiki/Divisibility_rule
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    Divisibility rule - Wikipedia

    https://en.wikipedia.org/wiki/Divisibility_rule

    A divisibility rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, or base, and they are all different, this article

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    The rules given below transform a given number into a generally smaller number, while preserving divisibility by the divisor of interest. Therefore, unless otherwise noted, the resulting number should be evaluated for divisibility by

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    Divisibility by 2
    First, take any number (for this example it will be 376) and note the last digit in the number, discarding the other digits. Then take that digit (6) while ignoring the rest of the number and determine if it is divisible by 2. If it is divisible by 2,

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    Divisibility properties of numbers can be determined in two ways, depending on the type of the divisor.
    Composite divisors
    A number is divisible by a

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    To test for divisibility by D, where D ends in 1, 3, 7, or 9, the following method can be used. Find any multiple of D ending in 9. (If D ends respectively in 1, 3, 7, or 9, then multiply by 9, 3, 7, or 1.) Then add 1 and divide by 10, denoting the result as m. Then a number N = 10t + q

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    • Apostol, Tom M. (1976). Introduction to analytic number theory. Undergraduate Texts in Mathematics. 1. Springer-Verlag. ISBN 978-0-387-90163-3.
    • Kisačanin, Branislav (1998). Mathematical problems and proofs: combinatorics, number theory, and geometry. Plenum

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    Proof using basic algebra
    Many of the simpler rules can be produced using only algebraic manipulation, creating binomialsand

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  4. Divisibility (ring theory) - Wikipedia

    https://en.wikipedia.org/wiki/Divisibility_(ring_theory)

    In mathematics, the notion of a divisor originally arose within the context of arithmetic of whole numbers. With the development of abstract rings, of which the integers are the archetype, the original notion of divisor found a natural extension.
    Divisibility is a useful concept for the analysis of the structure of commutative rings because of its relationship with the ideal structure of such rings.

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  5. Divisibility rules - Simple English Wikipedia, the free ...

    https://simple.wikipedia.org/wiki/Divisibility_rules

    Divisibility Rule of 4. The number formed by last 2 digits is divisible by 4. Eg:- 92, 780, 52, 300 Divisibility Rule of 5. When the ones digit of the number is either 0 or 5. Eg:- 55, 125, 1000, 760 Divisibility Rule of 6. A number is divisible by 6 if it is divisible by 2 and 3 also.

  6. divisibility - Wiktionary

    https://en.wiktionary.org/wiki/divisibility

    divisibility ( countable and uncountable, plural divisibilities ) ( uncountable) The state of being divisible. The state capable of being divided. ( arithmetic) The property of being divisible by a particular integer.

  7. Divisibilité — Wikipédia

    https://fr.wikipedia.org/wiki/Divisibilité
    • Dans l'ensemble des entiers naturels
      La notion de divisibilité est originaire de la notion de distribution en parts égales et est associée à la notion de division euclidienne : pour tous entiers naturels non nuls, a est divisible par b si et seulement si la division euclidienne de a par best exacte (i.e. a pour reste 0). La définition précé…
    • Dans l'ensemble des entiers relatifs
      La notion de divisibilité s'étend à l'ensemble des entiers relatifs en utilisant la même définition. On peut remarquer que a divise b si et seulement si |a| divise |b|. La relation « divise » dans l'ensemble des entiers relatifs possède presque les mêmes propriétés que dans l'ensemble des entiers natu…
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    • Divisibilidad - Wikipedia, la enciclopedia libre

      https://es.wikipedia.org/wiki/Divisibilidad
      • El número entero a {\displaystyle a} es divisible entre el número entero b ≠ 0 {\displaystyle b\neq 0} (o lo que es lo mismo, b divide a a) si hay un número q {\displaystyle q} entero, tal que a = b ⋅ q {\displaystyle a=b\cdot q} . Este hecho se denomina divisibilidad del número entero a {\displaystyle a} por el número entero b {\displaystyle b} y se denota por b | a {\displaystyle b|a} …
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      • Divisibility Rules | Prime Numbers Wiki | Fandom

        https://prime-numbers.fandom.com/wiki/Divisibility_Rules

        For explanation of each divisibility rules sorted by order, see List of Divisibility Rules. Divisibility rules are shorthand ways of division to tell if one number is divisible or not. They help tell whether the specific number you are looking for is prime or not. The many divisibility rules help many mathematicians and geniuses determine prime numbers, even if the number is beyond big. …

      • Divisibilidade – Wikipédia, a enciclopédia livre

        https://pt.wikipedia.org/wiki/Divisibilidade

        Divisibilidade. Origem: Wikipédia, a enciclopédia livre. Em aritmética e teoria dos números, diz-se que um número inteiro não nulo. a {\displaystyle a} divide um inteiro. b {\displaystyle b} , se existe um inteiro. c {\displaystyle c} , tal que.

      • Liste de critères de divisibilité — Wikipédia

        https://fr.wikipedia.org/wiki/Liste_de_critères_de_divisibilité
        • Lemmes de divisibilité par 7
          Première méthode : Un nombre est divisible par 7 si et seulement si la somme de son nombre de dizaines et de cinq fois son chiffre des unités l'est. On recommence jusqu'à ce que le nombre obtenu soit strictement inférieur à 56 (= 7 × 8). Le nombre est divisible par 7 si et seulement si l…
        • Critère pour un grand nombre
          Une méthode, basée seulement sur le fait que 103 est congru à –1 modulo 7, est de séparer ce nombre par tranches de 3 chiffres en partant des unités et d'insérer alternativement des – et des + entre les tranches. On effectue l'opération ainsi écrite et ce résultat est divisible par 7 si et seul…
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        • Criteri di divisibilità - Wikipedia

          https://it.wikipedia.org/wiki/Criteri_di_divisibilità

          In aritmetica, i criteri di divisibilità sono degli algoritmi che permettono di verificare la divisibilità di un numero intero per un fattore senza eseguire la divisione esplicita.. Consistono in una serie di operazioni sulle cifre che compongono il numero. Tali operazioni dovrebbero essere sufficientemente semplici da potersi fare a mente, o comunque essere più rapide rispetto alla



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