Question

Aplicando a decomposição em fatores primos, determine o Mdc entre os números: (a) 32 e 48 (b) 60 e 72 (c) 75 e 125 (d) 70,90 e 120 (e) 198,126 e 54 (f) 28,70e 84

Answer 1

a)
32,48/2
16,24/2
8,12/2
4,6/2
2,3/2
1,3/3
1

MDC de 32,48 = 2^4 = 16

b)
60,72/2
30,36/2
15,18/2
15/9/3
5,3/3
5,1/5
1,1

MDC de 60,70 = 2².3 = 12

c)
75,125/5
15,25/5
3,5/3
1,5/5
1,1
O MDC de 75,125 = 5² = 25

d)
70,90,120/2
35,45,60/2
35,45,30/2
35,45,15/5
7,9,3/3
7,3,1/3
7,1,1/7
1,1,1

O  MDC de 70,90,120 = 2 . 5 = 10

e)
198,126,54/2
99,63,27/3
33,21,9/3
11,7,3/3
11,7,1/7
11,1,1/11
1,1,1
O MDC de 198,126,54= 2. 3³ = 18

f)
28,70,84/2
14,35,42/2
7,35,21/3
7,35,7/5
7,7,7/7
1,1,1
O MDC de 28,70,84 = 2.7 = 14