Question

Calcule pela decomposição em fatores primos:
a)MDC (18,34)
b)MDC(30,45)
c)MDC(48,76)
d)MDC(64,98,120)

Answer 1

MDC(18, 34) = 2

MDC(30, 45) = 3 . 5 = 15

MDC(48, 76) = 22 = 4

MDC(64, 98, 120) = 2

Answer 2

a) 18 | 2
     9 | 3
     3 | 3
      1

34 | 2
17 | 17
  1

18 = 2.3.3
34 = 2.17
mdc(18,34) = 2
_________________
b) 30 | 2
    15 | 3
      5 | 5
      1

45 | 3
15 | 3
  5 | 5
  1
 30 = 2.3.5
45 = 3.3.5
mdc(30,45) = 3*5 = 15
___________________
c) 48 | 2
    24 | 2
    12 | 2
     6 | 2
     3 | 3
     1

76 | 2
38 | 2
19 | 19
1

48 = 2.2.2.2.3
76 = 2.2.19
mdc(48, 76) = 2*2 = 4
____________________
d) 64 | 2
    32 | 2
    16 | 2
     8 | 2
     4 | 2
     2 | 2
     1

98 | 2
49 | 7
  7 | 7
  1

120 | 2
  60 | 2
  30 | 2
  15 | 3
    5 | 5
    1

32 = 2.2.2.2.2
98 = 2.7.7
120 = 2.2.2.3.5
mdc(32,98,120) = 2