Divisibilidad

Divisibilidad

Múltiplos, divisores, números primos y factorización

A partir de la siguiente multiplicación:

3.5=15

decimos que:

3 es divisor de 15

5 es divisor de 15

15 es múltiplo de 3

15 es múltiplo de 5

  1. Sabiendo que:
    6.7=42
    ….. es múltiplo de ….. y de …..
    ….. y ….. son divisores de …..
  2. 1.10=10
    2.5=10
    ¿Cuáles son todos los divisores de 10?
  3. 13.1=13
    13,2=26
    13,3=39
    ¿Cuáles son los múltiplos de 13 menores que 100?
  4. ¿Por qué 12 es divisor de 36?
  5. ¿Por qué 56 es múltiplo de 4?
  6. Sabiendo que 85 es múltiplo de 17, ¿cuál es el siguiente múltiplo de 17?
  7. ¿Existe algún número natural que sea múltiplo de 6 y divisor de 36? ¿Cuál o cuáles?
  8. ¿Cuáles son todos los divisores de 40?
  9. ¿Cuáles son los múltiplos de 22 que están entre 200 y 350?
  10. Sabiendo que n representa a cualquier número natural y que:
  11. 1.n=n
    a) ……………….. es múltiplo de …………………
    b) ……………….. es múltiplo de …………………
    c) ……………….. es divisor de …………………
    d) ……………….. es divisor de …………………
  12. Sabiendo que n representa a cualquier número natural y que:
    0.n=0
    a) ……………….. es múltiplo de …………………
    b) ……………….. es múltiplo de …………………
    c) ……………….. es divisor de …………………
    d) ……………….. es divisor de …………………
  13. Un número natural es primo, si sólo tiene 2 divisores.
    ¿Cuáles son los números primos menores que 40?
  14. La factorización de la que hablaremos es aquella en la que todos los factores son números primos. Factoricen los siguientes números naturales:
    a) 24
    b) 90
    c) 164
    d) 320
  15. Busquen tres números que en su factorización tengan al menos un 2, un 3 y un 5.

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wolf-divisores

Divisores con wolframalpha

Para buscar los divisores de un número natural con WolframAlpha

Escribimos:

Y obtenemos.

Por ejemplo, los divisores de 36 son nueve: 1, 2, 3, 4, 6, 9, 12, 18 y 36

También vemos la descomposición en factores primos de 36: 2^2.3^2

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Problema

Para armar ofertas de golosinas, don Héctor cuenta con 60 chupetines, 75 galletitas con chocolate y 120 caramelos. Quiere armar bolsitas iguales que contengan el mayor número posible de cada cosa.
¿Cómo pueden averiguar las cantidades?¿Cuántas bolsitas se pueden armar?

———…———-

Número de Visitas: 3782


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División entera y división exacta

Una división es entera cuando el cociente y el resto de la misma son números enteros.

Ejemplo:   13 : 2 = 6 con resto 1
Dividendo -> 13
Divisor -> 2
Cociente -> 6
Resto -> 1

Además:
13 = 2 . 6 + 1
D = d . c + r

En toda división entera el resto es mayor o igual que cero y menor que el divisor.
0 ≤ r < d

Una división entera es exacta cuando el resto de la división es cero.

Ejemplo:    21 : 3 = 7 con resto 0
Además 21 =  3 . 7

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