Question

1-Determine o MDC (máximo divisor comum) entre os números abaixo:
a)mdc(2,8)
b)mdc(3,20)
c)mdc(16,4,8)
d)mdc(5,4)
e)mdc(4,18)
f)mdc(5,6,2)
g)mdc(4,10)
h)mdc(30,8)
i)mdc(8,36,40)

Answer 1

1) a) 2, 8 | 2

1, 4 | 2

1, 2 | 2

1, 1 | 1

MMC = 2 . 2 . 2 = 8

MDC(2, 8) = 2

b) 3, 20 | 2

3, 10 | 2

3, 5 | 3

1, 5 | 5

1, 1 | 1

MMC = 2 . 2 . 3 . 5 = 60

MDC(3, 20) = 1

c) 16, 4, 8 | 2

8, 2, 4 | 2

4, 1, 2 | 2

2, 1, 1 | 2

1, 1, 1 | 1

MMC = 2 . 2 . 2 . 2 = 16

MDC(16, 4, 8) = 22 = 4

d) 5, 4 | 2

5, 2 | 2

5, 1 | 5

1, 1 | 1

MMC = 2 . 2 . 5 = 20

MDC(5, 4) = 1

e) 4, 18 | 2

2, 9 | 2

1, 9 | 3

1, 3 | 3

1, 1 | 1

MMC = 2 . 2 . 3 . 3 = 36

MDC(4, 18) = 2

f) 5, 6, 2 | 2

5, 3, 1 | 3

5, 1, 1 | 5

1, 1, 1 | 1

MMC = 2 . 3 . 5 = 30

MDC(5, 6, 2) = 1

g) 4, 10 | 2

2, 5 | 2

1, 5 | 5

1, 1 | 1

MMC = 2 . 2 . 5 = 20

MDC(4, 10) = 2

h) 30, 8 | 2

15, 4 | 2

15, 2 | 2

15, 1 | 3

5, 1 | 5

1, 1 | 1

MMC = 2 . 2 . 2 . 3 . 5 = 120

MDC(30, 8) = 2

i) 8, 36, 40 | 2

4, 18, 20 | 2

2, 9, 10 | 2

1, 9, 5 | 3

1, 3, 5 | 3

1, 1, 5 | 5

1, 1, 1 | 1

MMC = 2 . 2 . 2 . 3 . 3 . 5 = 360

MDC(8, 36, 40) = 22 = 4