Respuestas
Respuesta dada por:
1
Descomponemos el número:
462=2*3*7*11
Suma de divisores:
Si:
![N=a^{x}*b^{y}*c^{z} *... N=a^{x}*b^{y}*c^{z} *...](https://tex.z-dn.net/?f=N%3Da%5E%7Bx%7D%2Ab%5E%7By%7D%2Ac%5E%7Bz%7D+%2A...)
![SD= (\frac{ a^{x+1}-1}{a-1})*(\frac{ b^{y+1}-1}{b-1})*(\frac{ c^{z+1}-1}{c-1})*... SD= (\frac{ a^{x+1}-1}{a-1})*(\frac{ b^{y+1}-1}{b-1})*(\frac{ c^{z+1}-1}{c-1})*...](https://tex.z-dn.net/?f=SD%3D+%28%5Cfrac%7B+a%5E%7Bx%2B1%7D-1%7D%7Ba-1%7D%29%2A%28%5Cfrac%7B+b%5E%7By%2B1%7D-1%7D%7Bb-1%7D%29%2A%28%5Cfrac%7B+c%5E%7Bz%2B1%7D-1%7D%7Bc-1%7D%29%2A...)
Entonces:
![SD(462)=(\frac{2^{1+1}-1}{2-1})*(\frac{3^{1+1}-1}{3-1})*(\frac{7^{1+1}-1}{7-1})*(\frac{11^{1+1}-1}{11-1}) SD(462)=(\frac{2^{1+1}-1}{2-1})*(\frac{3^{1+1}-1}{3-1})*(\frac{7^{1+1}-1}{7-1})*(\frac{11^{1+1}-1}{11-1})](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)
![SD(462)=(\frac{2^{2}-1}{1})*(\frac{3^{2}-1}{2})*(\frac{7^{2}-1}{6})*(\frac{11^{2}-1}{10}) SD(462)=(\frac{2^{2}-1}{1})*(\frac{3^{2}-1}{2})*(\frac{7^{2}-1}{6})*(\frac{11^{2}-1}{10})](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)
![SD(462)=(4-1)*(\frac{9-1}{2})*(\frac{49-1}{6})*(\frac{121-1}{10}) SD(462)=(4-1)*(\frac{9-1}{2})*(\frac{49-1}{6})*(\frac{121-1}{10})](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)
![SD(462)=(3)*(\frac{8}{2})*(\frac{48}{6})*(\frac{120}{10}) SD(462)=(3)*(\frac{8}{2})*(\frac{48}{6})*(\frac{120}{10})](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)
![SD(462)=(3)*(4)*(8)*(12) SD(462)=(3)*(4)*(8)*(12)](https://tex.z-dn.net/?f=SD%28462%29%3D%283%29%2A%284%29%2A%288%29%2A%2812%29)
![SD(462)=1152 SD(462)=1152](https://tex.z-dn.net/?f=SD%28462%29%3D1152)
Por lo tanto, la suma de los divisores de 462 es 1152.
462=2*3*7*11
Suma de divisores:
Si:
Entonces:
Por lo tanto, la suma de los divisores de 462 es 1152.
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