Question

Aplicando a decomposição em fatores primos determine o m.d.c entre os números:
A)32e48
B)60e72
C)75e125
D)70,90e120
E)198,126e54
F)28,70e84

Answer 1

OI..

Entendamos que o MDC são fatores comuns de menores expoentes.

O MDC de:

a)

32,48/2

18,24/2

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)

70,90,120/2

35,45,60/2

35,45,30/2

35,45,15/3

35,15,5/3

35,5,5/5

7,1,1/7

1,1,1

MDC = 2.5 = 10

MDC = 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

MDC = 2.3.3 = 18

MDC = 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

MDC = 2.7 = 14

MDC = 14

Espero ter ajudado.