Determine o Mdc de a)32,48. b)60,72. c)75,125. d)79,30,120. e)198,196,54. f)28,70,84. Porfavor e Pra Hoje!
Respostas
Olá...
O MDC são fatores comuns de menores expoentes.
MDC de:
a)
32,48/2
16,24/2
8,12/2
4,6/2
2,3/2
1,3/3
1,1
MDC = 2.2.2.2 = 16
MDC = 16
b)
60,72/2
30,36/2
15,18/2
15,9/3
5,3/3
5,1/5
1,1
MDC = 2.2.3 = 12
MDC = 12
c)
75,125/3
25,125/5
5,25/5
1,5/5
1,1
MDC = 5.5 = 25
MDC = 25
d)
79,30,120/2
79,15,60/2
79,15,30/2
79,15,15/3
79,5,5/5
79,1,1/79
1,1,1
MDC = 1
e)
198,196,54/2
99,98,27/2
99,49,27/3
33,49,9/3
11,49,3/3
11,49,1/7
11,7,1/7
11,1,1/11
1,1,1
MDC = 2
f)
28,70,84/2
14,35,42/2
7,35,21/3
7,35,7/5
7,7,7/7
1,1,1
MDC = 2.7 = 14
MDC = 14
Espero ter ajudado.
Resposta:
Explicação passo-a-passo:
.. a) m.d.c (32, 48) = 16 b) m.d.c. (60, 72) = 12
.. 32, 48 l 2 (*) 60, 72 l 2 (*)
.. 16, 24 l 2 (*) 30, 36 l 2 (*)
.. 8, 12 l 2 (*) 15, 18 l 2
.. 4, 6 l 2 (*) 15, 9 l 3 (*)
.. 2, 3 l 2 5, 3 l 3
.. 1, 3 l 3 5, 1 l 5
.. 1, 1 l (*) = fator comum
c) m.d.c. (75, 125) = 25 d) m.d.c. (79, 30, 120) = 1
. 75, 125 l 3 79, 30, 120 l 2
. 25, 125 l 5 (*) 79, 15, 60 l 2
. 5, 25 l 5 (*) 79, 15, 30 l 2
. 1, 5 l 5 79, 15, 15 l 3
. 1, 1 l 79, 5, 5 l 5
79, 1, 1 l 79
. 1, 1, 1 l
e) m.d.c.(198, 196, 54) = 2 f) m.d.c.(28, 70, 84) = 14
. 198, 196, 54 l 2 (*) 28, 70, 84 l 2 (*)
. 99, 98, 27 l 2 14, 35, 42 l 2
. 99, 49, 27 l 3 7, 35, 21 l 3
. 33, 49, 9 l 3 7, 35, 7 l 5
. 11, 49, 3 l 3 7, 7, 7 l 7 (*)
. 11, 49, 1 l 7 1, 1, 1 l
. 11, 7, 1 l 7
. 11, 1, 1 l 11
. 1, 1, 1 l