Question

Pelo processo das divisões sucessivas, determine o m.d.c. de: A: m.d.c.(160, 80) B: m.d.c.(50, 12) C: m.d.c.(12, 5) D: m.d.c.(24, 18, 12)

Answer 1

a) MDC (160, 80) = 80

160, 80 | 2

80, 40 | 2

40, 20 | 2

20, 10 | 2

10, 5 | 2

5, 5 | 5

1, 1

2 . 2 . 2 . 2 . 5 = 2² . 2² . 5 = 4 . 4 . 5 = 16 . 5 = 80

b) MDC (50, 12) = 2

50, 12 | 2

25 , 6 | 2

25, 3 | 3

25 , 1 | 5

5, 1 | 5

1, 1

c) MDC (12, 5) = 1

12, 5 | 2

6, 5 | 2

3, 5 | 3

1, 5 | 5

1, 1

1

d) MDC (24, 18, 12) = 6

24, 18, 12 | 2

12, 9, 6 | 2

6, 9, 3 | 2

3, 9, 3 | 3

1, 3, 1 | 3

1, 1, 1

2 . 3 = 6