cualquier número compuesto se puede expresar como un producto de números primos

obtenga cualquier número compuesto se puede expresar como un producto de números primos de este sitio.

Números compuestos

Números compuestos   Un número compuesto es el que posee más de dos divisores. Es decir, aquel que se puede dividir por sí mismo, por la unidad y por otros números. Ejemplos: 12 = 2 · 2 · 3 72 = 2 · 4 · 9 144 = 2 ·…

Números compuestos

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Factorizar un número

Un número compuesto es el que posee más de dos divisores. Es decir, aquel que se puede dividir por sí mismo, por la unidad y por otros números.

Ejemplos: 12 = 2 · 2 · 3 72 = 2 · 4 · 9 144 = 2 · 6 · 12

Los números compuestos se pueden expresar como productos de potencias de números primos. A dicha expresión se le llama descomposición de un número en factores primos.

Ejemplos: 12 = 2² · 3 72 = 2³ · 3² 144 = 24 · 3²

Factorizar un número

Para factorizar un número o descomponerlo en factores efectuamos sucesivas divisiones entre sus divisores primos hasta obtener un 1 como cociente.

Para factorizar utilizaremos una barra vertical, a la derecha escribimos los divisores primos y a la izquierda las sucesivas divisiones.

Ejemplo: 1Factorizar 2520

Como el número termina en cifra par es divisible por 2, colocamos el 2 a la derecha de la raya

Dividimos 2520 por 2 y lo colocamos a la izquierda

1260 termina en 0, por tanto también es divisible por 2, colocamos el 2 a la derecha de la raya

Dividimos 1260 por 2 y lo colocamos a la izquierda

630 termina en 0, por tanto también es divisible por 2, colocamos el 2 a la derecha de la raya

Dividimos 630 por 2 y lo colocamos a la izquierda

Como no to termina en cifra par ni en 0 no es divisible por 2, entonces probamos por 3. La suma de las cifras de 315 es igual a 9 que divisible por 3. Colocamos el 3 a la derecha de la raya

Dividimos 315 por 3 y lo colocamos a la izquierda

Volvemos a probar por 3. La suma de las cifras de 105 es igual a 6 que divisible por 3. Colocamos el 3 a la derecha de la raya

Dividimos 105 por 3 y lo colocamos a la izquierda

Volvemos a probar por 3. La suma de las cifras de 35 es igual a 8 que no es divisible por 3, por tanto tenemos que probar por el siguiente número primo que es 5, como 35 termina en 5 es divisible entre 5. Colocamos el 5 a la derecha de la raya

Dividimos 35 por 5 y lo colocamos a la izquierda

7 es un número primo, por tanto es divisible por sí mismo. Colocamos el 7 a la derecha de la raya

Dividimos 7 por 7 y lo colocamos a la izquierda

Una vez que llegamos a 1 termina la factorización

Como a la derecha tenemos el 2 repetido tres veces, el 3 repetido dos veces, el 5 y el 7; la factorización será:

Solución:   2 520 = 2³ · 3² · 5 · 7

2Factorizar 432 Ejemplo:

Solución: 432 = 24 · 3³

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Resumen

Resumen de divisibilidad

Teoría

Divisores

Criterios de divisibilidad

Maximo comun divisor

¿Qué es un Múltiplo?

Maximo comun divisor y minimo comun multiplo

Algoritmo de Euclides

Minimo comun multiplo

Numeros primos

Ejercicios interactivos

Ejercicios interactivos de múltiplos

Ejercicios interactivos de las propiedades de los múltiplos

Ejercicios interactivos de divisores

Ejercicios interactivos de las propiedades de los divisores

Ejercicios interactivos de criterios de divisiblidad

Ejercicios interactivos de numeros compuestos

Ejercicios interactivos de maximo comun divisor

Ejercicios interactivos del mínimo común múltiplo

Ejercicios interactivos de numeros primos

Ejercicios interactivos del algoritmo de Euclides

Otros ejercicios

Problemas de mcd y mcm

Ejercicios de divisibilidad

Apuntes es una plataforma dirigida al estudio y la práctica de las matemáticas a través de la teoría y ejercicios interactivos que ponemos a vuestra disposición. Esta información está disponible para todo aquel/aquella que quiera profundizar en el aprendizaje de esta ciencia. Será un placer ayudaros en caso de que tengáis dudas frente algún problema, sin embargo, no realizamos un ejercicio que nos presentéis de 0 sin que hayáis si quiera intentado resolverlo. Ánimo, todo esfuerzo tiene su recompensa.

Déjanos un comentario

Camila Noviembre 2021

Woow increible esto merece un crédito, si verdaderamente lo necesita escríbame, espero tenga buen día!

Eimi cuevas carvajar

Febrero 2022 Hola Camila 💕 deicy fernandez Octubre 2021 muy completo Javier Marzo 2022 Ese si es verdad Hola es bueno Ángela Abril 2021

Hola! creo que hay un error cuando dices que la suma de las cifras 35 es igual a 7, sería 8,no? entonces como seguiría el problema?

Gracias, un saludo 🙂

Superprof Septiembre 2021 Hola, Ángela:

La resolución sería igual, ha sido solo una errata que ya hemos corregido 🙂

Gracias por tu comentario ❤️

Alondra Marzo 2021

Hola Buenas, me gustó este artículo pero yo hubiese puesto más información para que el que visite todo esto sepa más cosas

enmanuel Febrero 2021

pero es muy educatibo es bueno para el zerebro

Kamila Agosto 2021

es cerebro y educativo

fuente : www.superprof.es

Número compuesto

Solemos invitar al mundo a crear la suma de todo el conocimiento humano. En esta ocasión, invitamos al mundo a crear el sonido de todo el conocimiento humano.

[¡Ayúdanos con las traducciones!]

Número compuesto

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Números naturales de cero a cien. Los números compuestos está caducados en verde.

Número compuesto es cualquier número natural no primo, a excepción del 1. Es decir, tiene uno o más divisores distintos a 1 y a sí mismo. También se utiliza el término divisible para referirse a estos números.

Los treinta primeros números compuestos son: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44 y [[cuarenta y cinco|45

Recuerda

Los números compuesto son los que llevan más de 2 n Números Y los primos son los que llevan 2 digitos por ejemplo el 1 y el mismo por ejemplo el 12

Características[editar]

Artículo principal:

Una característica es que cada uno puede escribirse como producto de dos números naturales menores que él.Así, el número 20 es compuesto porque puede expresarse como 4×5; y también el 87 ya que se expresa como 3×29. Sin embargo, no es posible hacer lo mismo con el 17 o el 23 porque son números primos. Cada número compuesto se puede expresar como multiplicación de dos (o más) números primos específicos, cuyo proceso se conoce como factorización. El número compuesto más pequeño es el 4.

La forma más sencilla para probar que un número es compuesto, es encontrar un divisor comprendido entre 1 y (1 < < ). Por ejemplo, 219 es compuesto porque tiene a 3 por divisor. Y también 371 porque tiene a 7 por divisor. Una buena alternativa es utilizar entonces el pequeño teorema de Fermat, o mejor la generalización de este teorema debida al matemático suizo Leonhard Euler.

Como los números primos y compuestos están entremezclados unos con otros es lógico preguntarse si existirán secuencias de números compuestos consecutivos de longitud arbitraria. La secuencia 32, 33, 34, 35 y 36 es un ejemplo de longitud 5, y 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125 y 126 un ejemplo de longitud 13. La respuesta es que podemos conseguir una secuencia de números compuestos tan larga como se desee. Si deseamos una secuencia de longitud 20, basta tomar los números 21!+2, 21!+3, 21!+4, ... , 21!+21, ya que el primero es divisible por 2, el segundo por 3, etcétera.

Un teorema de Fermat afirma que si es primo de la forma 4+1, entonces se da un caso de exclusión simple, que puede expresarse de forma única como suma de dos cuadrados. Si un número de la forma 4n+1 puede expresarse como suma de dos cuadrados de dos formas diferentes al menos, entonces el número es compuesto. Euler halló un método de factorización a partir de este hecho. Por ejemplo, si 221 = 112 + 102 = 142 + 52, entonces, 142 - 112 = 102 - 52. Tomando mcd(14+11, 10+5) = mcd(25,15) = 5, y después 25/5 = 5 y 15/5 = 3, y por último 52 + 32 = 25 + 9 = 34, entonces mcd(221, 34) = 17 nos da el factor que buscamos. El 1 y el 0 son casos especiales y no se consideran ni primos ni compuestos.

Véase también[editar]

Clasificación de los números

Complejos

{\displaystyle :\;\mathbb {C} }

Reales

{\displaystyle :\;\mathbb {R} }

Racionales

{\displaystyle :\;\mathbb {Q} }

Enteros

{\displaystyle :\;\mathbb {Z} }

Naturales

{\displaystyle :\;\mathbb {N} }

uno: 1 Naturales primos

Naturales compuestos

Cero: 0 Enteros negativos Fraccionarios Exactos Periódicos Puros Mixtos Irracionales

Irracionales algebraicos

Trascendentes Imaginarios

Enlaces externos[editar]

Weisstein, Eric W. «Composite Number». En Weisstein, Eric W, ed. (en inglés). Wolfram Research.

Control de autoridades

Proyectos WikimediaDatos: Q50707Diccionarios y enciclopediasBritannica: url

Datos: Q50707

Categorías: Sucesiones de números enterosNúmeros enteros

fuente : es.wikipedia.org

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248px}}@media(max-width:767px){.sg-toplayer--small-spaced{margin-left:24px;margin-right:24px;margin-top:96px;max-width:336px}}.sg-toplayer--splash-screen{margin:12px;min-height:100%;min-height:calc(100% - 24px);overflow:hidden}@media(min-width:768px){.sg-toplayer--splash-screen{margin:24px;min-height:calc(100% - 48px)}}.sg-toplayer--limited-width{max-width:1024px}.sg-toplayer--row{flex-direction:row}.sg-toplayer__close{cursor:pointer;display:flex;padding:12px;position:absolute;right:0;top:0;z-index:1}.sg-toplayer__wrapper{padding:1.5rem 24px;width:100%}.sg-toplayer__wrapper--no-padding{padding:0}.sg-toplayer__actions{align-items:center;display:flex;flex-wrap:wrap;min-height:3rem}.sg-dropdown{align-items:center;-webkit-appearance:none;appearance:none;background-color:#ebf2f7;border:2px solid #ebf2f7;border-radius:50px;cursor:pointer;display:inline-flex;font-size:.9375rem;height:40px;justify-content:space-between;line-height:1.25rem;min-height:40px;outline:0;padding:0 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fuente : brainly.lat