Question

Determinați Nr Nat de forma 28ab14, divizibile cu 14! HELP PLS

Answer 1

$\overline{28ab14}=280000+ 100 \cdot \overline{ab}+14=280014+100 \cdot \overline{ab}. \\ \\ 280014 ~ \vdots~14 \Rightarrow100 \cdot \overline{ab} ~ \vdots~14,~dar~(100;14)=2 \Rightarrow~ \overline{ab}~ \vdots~7. \\ \\ Deci~ \overline{ab} \in \{14,21,28,35,42,49,56,63,70,77,84,91,98 \}. \\ \\ Deci~in~total~exista~13~astfel~de~numere.$

$281414~;~282114~;~282814~;~283514~;~284214~;~284914~;~285614~;~ \\ \\ 286314~;~287014~;~287714~;~288414~;~289114~;~289814.$