Question

A12b divizibil cu 12
a;b=.

Answer 1

Explicație pas cu pas:

12 = 4×3

(4;3) = 1 => divizibil cu 4 și divizibil cu 3

$\overline {a12b} \ \ \vdots \ \ 4 \implies b \in \Big\{ 0; 4; 8\Big\}$

$\overline {a12b} \ \ \vdots \ \ 3 \implies (a + 1 + 2 + b) \ \ \vdots \ \ 3 \iff (a + b) \ \ \vdots \ \ 3$

$b = 0 \iff (a + 0) \ \ \vdots \ \ 3 \iff a \in \Big\{ 3; 6; 9\Big\} \\ \implies \overline {a12b} \in \Big\{ 3120; 6120; 9120\Big\} \\ b = 4 \iff (a + 4) \ \ \vdots \ \ 3 \iff a \in \Big\{ 2; 5; 8\Big\} \\ \implies \overline {a12b} \in \Big\{ 2124; 5124; 8124\Big\} \\ b = 8 \iff (a + 8) \ \ \vdots \ \ 3 \iff a \in \Big\{ 1; 4; 7\Big\} \\ \implies \overline {a12b} \in \Big\{ 1128; 4128; 7128\Big\}$