The natural numbers $x$ and $y$ satisfy the relation $2 x=7 y$.

a) Determine $x$ and $y$ knowing that their product is 2016.

b) Determine $x$ and $y$ knowing that their greatest common divisor is 11.
a) Since $2 \mid 7 y$ it follows that $2 \mid y, y=2 k$, then $x=7 k, k \in \mathbb{N}^{*}$ and $x y=14 k^{2}=2016$ $3 \mathrm{p}$

$k^{2}=144, k=12, x=84, y=24$

b) Since $\quad x=7 k, y=2 k, k \in \mathbb{N}^{*},(x, y)=k$, it follows that $k=11, x=77, y=22$