Respostas

2014-01-15T22:31:42-02:00
Nos itens a seguir, determine as fatorações dos números apresentados, bem como seu mdc e mmc

(414 e 84)

414, 84 | 2
207, 42 | 2
207, 21 | 3
69,    7 | 3
23,    7 | 7
23,    1 | 23
 1,     1

414 , 84 = 2² * 3² * 7 * 23 = 5.796
mmc (414, 84) = 5.796

D (414) = {1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414}
D (84) = {1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84}
D (414) ∩ D (84) = {1, 2, 3, 6}
mdc (414, 84) = 6

(1617 e 750)

1617, 750 | 2
1617, 375 | 3
  539, 125 | 5
  539,   25 | 5
  539,    5  | 5
  539,    1  | 7
   77,     1  | 7
   11,      1 | 11
    1

1617, 750 =  2 . 3 . 5³ . 7² . 11
mmc (1617, 750) = 2 . 3 . 5³ . 7² . 11
mmc (1617, 750) = 2 . 3 . 125 . 49 . 11
mmc (1617, 750) = 404.250

D (1617) = {1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, 1617}
D (750) = {1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750}
D (1617) ∩ D (750) = {1, 3}
mdc (1617, 750) = 3

(65 e 220) 

65, 220 | 2
65, 110 | 2
65,  55 | 5
13,  11 | 11
13,   1  | 13
 1,    1

65, 220 = 2² * 5 * 11 * 13 
mmc (65, 220) = 2² * 5 * 11 * 13 
mmc (65, 220) = 4 * 5 * 11 * 13
mmc (65, 220) = 2860

D (65) = {1, 5, 13, 65}
D (220) = {1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220}
D (65) ∩ D (220) = {1, 5}
mdc (65, 220) = 5

(247 e 231)

247, 231 | 3
247,  77 | 7
247,  11 | 11
247,    1 | 13
  19,    1 | 19
    1,    1

247, 231 = 3 * 7 * 11 * 13 * 19
mmc (247, 231) = 3 * 7 * 11 * 13 * 19
mmc (247, 231) = 57057

D (247) = {1, 13, 19, 247}
D (231) = {1, 3, 7, 11, 21, 33, 77, 231}
D (231) ∩ (247) = {1}
mdc (231, 247) = 1
1 5 1