Question

Urgente!! MDC de:
45,75 e 125=
84 e 126=
132 e 210=
78,130 e 156=
36,42 e 55=

Answer 1

Para determinar o MDC, fatoramos todos números simultaneamente (semelhante ao MMC), destacando sempre o fator que for comum a todos os números.

O MDC será o produto de todos fatores comuns (destacados).

a)

$45~,~75~,~125~~|~~3\\15~,~25~,~125~~|~~3\\05~,~25~,~125~~|~~\boxed{5}\\~~\,1~,~~\,5~,~~\,25~~|~~5\\~~\,1~,~~\,1~,~~~~5~~|~~5\\~~\,1~,~~\,1~,~~~~1~~|~~\boxed{1}\\\\\\MDC(45,75,125)~=~5~.~1\\\\\boxed{MDC(45,75,125)~=~5}$

b)

$84~,~126~~|~~\boxed{2}\\42~,~~\,63~~|~~2\\21~,~~\,63~~|~~\boxed{3}\\~~\,7~,~~\,21~~|~~3\\~~\,7~,~~~~7~~|~~\boxed{7}\\~~\,1~,~~~~1~~|~~\boxed{1}\\\\\\MDC(84,126)~=~2~.~3~.~7~.~1\\\\\\\boxed{MDC(84,126)~=~42}$

c)

$132~,~210~~|~~\boxed{2}\\~~\,66~,~105~~|~~2\\~~\,33~,~105~~|~~\boxed{3}\\~~\,11~,~~\,35~~|~~5\\~~\,11~,~~~~7~~|~~7\\~~\,11~,~~~~1~~|~~11\\~~~~1~,~~~~1~~|~~\boxed{1}\\\\\\MDC(132,210)~=~2~.~3~.~1\\\\\\\boxed{MDC(132,210)~=~6}$

d)

$78~,~130~,~156~~|~~\boxed{2}\\39~,~~\,65~,~~\,78~~|~~2\\39~,~~\,65~,~~\,39~~|~~3\\13~,~~\,65~,~~\,13~~|~~5\\13~,~~\,13~,~~\,13~~|~~\boxed{13}\\~~\,1~,~~~~1~,~~~~1~~|~~\boxed{1}\\\\\\MDC(78,130,156)~=~2~.~13~.~1\\\\\\\boxed{MDC(78,130,156)~=~26}$

e)

$36~,~42~,~55~~|~~2\\18~,~21~,~55~~|~~2\\~~\,9~,~21~,~55~~|~~3\\~~\,3~,~~\,7~,~55~~|~~3\\~~\,1~,~~\,7~,~55~~|~~5\\~~\,1~,~~\,7~,~11~~|~~7\\~~\,1~,~~\,1~,~11~~|~~11\\~~\,1~,~~\,1~,~~\,1~~|~~\boxed{1}\\\\\\\boxed{MDC(36,42,55)~=~1}$