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La suma de divisores de 462?

La suma de divisores de 462.

En resumen

Descomponemos el número : 462 = 2 * 3 * 7 * 11 Suma de divisores : Si : <img src="https://tex.z-dn.net/?f=N%3Da%5E%7Bx%7D%2Ab%5E%7By%7D%2Ac%5E%7Bz%7D%20%2A..." /> <img src="https://tex.z-dn.net/?

Mejor respuesta

Katheling
6

Descomponemos el número :

462 = 2 * 3 * 7 * 11

Suma de divisores :

Si :

<img src="https://tex.z-dn.net/?f=N%3Da%5E%7Bx%7D%2Ab%5E%7By%7D%2Ac%5E%7Bz%7D%20%2A..." />

<img src="https://tex.z-dn.net/?f=SD%3D%20%28%5Cfrac%7B%20a%5E%7Bx%2B1%7D-1%7D%7Ba-1%7D%29%2A%28%5Cfrac%7B%20b%5E%7By%2B1%7D-1%7D%7Bb-1%7D%29%2A%28%5Cfrac%7B%20c%5E%7Bz%2B1%7D-1%7D%7Bc-1%7D%29%2A..." />

Entonces :

<img src="https://tex.z-dn.net/?f=SD%28462%29%3D%28%5Cfrac%7B2%5E%7B1%2B1%7D-1%7D%7B2-1%7D%29%2A%28%5Cfrac%7B3%5E%7B1%2B1%7D-1%7D%7B3-1%7D%29%2A%28%5Cfrac%7B7%5E%7B1%2B1%7D-1%7D%7B7-1%7D%29%2A%28%5Cfrac%7B11%5E%7B1%2B1%7D-1%7D%7B11-1%7D%29" />

<img src="https://tex.z-dn.net/?f=SD%28462%29%3D%28%5Cfrac%7B2%5E%7B2%7D-1%7D%7B1%7D%29%2A%28%5Cfrac%7B3%5E%7B2%7D-1%7D%7B2%7D%29%2A%28%5Cfrac%7B7%5E%7B2%7D-1%7D%7B6%7D%29%2A%28%5Cfrac%7B11%5E%7B2%7D-1%7D%7B10%7D%29" />

<img src="https://tex.z-dn.net/?f=SD%28462%29%3D%284-1%29%2A%28%5Cfrac%7B9-1%7D%7B2%7D%29%2A%28%5Cfrac%7B49-1%7D%7B6%7D%29%2A%28%5Cfrac%7B121-1%7D%7B10%7D%29" />

<img src="https://tex.z-dn.net/?f=SD%28462%29%3D%283%29%2A%28%5Cfrac%7B8%7D%7B2%7D%29%2A%28%5Cfrac%7B48%7D%7B6%7D%29%2A%28%5Cfrac%7B120%7D%7B10%7D%29" />

<img src="https://tex.z-dn.net/?f=SD%28462%29%3D%283%29%2A%284%29%2A%288%29%2A%2812%29" />

<img src="https://tex.z-dn.net/?f=SD%28462%29%3D1152" />

Por lo tanto, la suma de los divisores de 462 es 1152.