Let $a,b \in \mathbb{N}$ such that $2a=3b$. Show that $2|b$ and $3|a$.
My Approach:
My approach to this question is to find an expression for $b$ in a way that the expression is divisible by $2$. Then, find an expression for $a$ in such a way that the expression is divisible by $3$. I tried several calculations but none of them seems to go anywhere.
Since 2 divides 3b, either 2 divides 3 or 2 divides b. Since 2 doesn't divide 3, 2 must divide b.