Question

a) mdc (15'40) c) mdc (85,75)
b) mdc (22,46) d) mdc (20,130)​

Answer 1

Olá...

Calcule o MDC de:

a)

15, 40 | 2

15, 20 | 2

15, 10 | 2

15, 5 | 3

5, 5 | 5

1, 1

MDC = 5

b)

22, 46 | 2

11, 23 | 11

1, 23 | 23

1, 1

MDC = 2

c)

85, 75 | 3

85, 25 | 5

17, 5 | 5

17, 1 | 17

1, 1

MDC = 5

d)

20, 130 | 2

10, 65 | 2

5, 65 | 5

1, 13 | 13

1, 1

MDC = 2 . 5 = 10

Espero ter ajudado.

Answer 2

Para determinar o MDC, fatoramos os números simultaneamente (semelhante ao MMC) e destacamos os fatores que forem comuns a todos.

O MDC será o produto desses fatores comuns.

a)

$15~,~40~~|~~2\\15~,~20~~|~~2\\15~,~10~~|~~2\\15~,~~\,5~~|~~3\\~~\,5~,~~\,5~~|~~\boxed{5}\\~~\,1~,~~\,1~~|~~\boxed{1}\\\\\\MDC(15,40)~=~5~.~1\\\\\boxed{MDC(15,40)~=~5}$

b)

$85~,~75~~|~~3\\85~,~25~~|~~\boxed{5}\\17~,~~\,5~~|~~5\\17~,~~\,1~~|~~17\\~~\,1~,~~\,1~~|~~\boxed{1}\\\\\\MDC(85,75)~=~5~.~1\\\\\boxed{MDC(85,75)~=~5}$

c)

$22~,~46~~|~~\boxed{2}\\11~,~23~~|~~11\\~~\,1~,~23~~|~~23\\~~\,1~,~~\,1~~|~~\boxed{1}\\\\\\MDC(22,46)~=~2~.~1\\\\\boxed{MDC(22,46)~=~2}$

d)

$20~,~130~~|~~\boxed{2}\\10~,~~\,65~~|~~2\\~~\,5~,~~\,65~~|~~\boxed{5}\\~~\,1~,~~\,13~~|~~13\\~~\,1~,~~~~1~~|~~\boxed{1}\\\\\\MDC(20,130)~=~2~.~5~.~1\\\\\boxed{MDC(20,130)~=~10}$