Question

Ex:2

Dar sa fie putin explicit!

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Answer 1

   
[tex]63:n=c_1 ~\texttt{rest}~3 \Rightarrow 63 = n\times c_1+3 \\ \Rightarrow 63-3 = n\times c_1\Rightarrow (63-3):n=c_1\Rightarrow \boxed{(63-3)~\vdots~ n}\\\\\\ 124:n=c_2 ~\texttt{rest}~4 \Rightarrow 124 = n\times c_2+4 \\ \Rightarrow 124-4 = n\times c_2\Rightarrow (124-4):n=c_2\Rightarrow \boxed{(124-4)~\vdots~ n}\\\\\\ 155:n=c_3 ~\texttt{rest}~5 \Rightarrow 155 = n\times c_3+4 \\ \Rightarrow 155-5 = n\times c_3\Rightarrow (155-5):n=c_2\Rightarrow \boxed{(155-5)~\vdots~ n}\\\\\\ [/tex]


[tex]\Longrightarrow~~ n = \texttt{cmmdc}\{(63-3),~(124-4),~(155-5)\}\\ \Longrightarrow~~ n = \texttt{cmmdc}\{60;~120;~150\}\\\\ \texttt{Descompunem numerele in factori primi.}\\\\ 60 = 2^2\times 3\times 5\\ 120=2^3\times 3\times 5\\ 150=2\times 3\times 5^2\\\\ n= \texttt{cmmdc} = 2\times 3\times 5 = 30\\\\ \text{Solutia: }~ \boxed{\bf n = 30}[/tex]