Every group is a quotient of a residually finite group

Statement
Let $$G$$ be a group. Then, there exists a residually finite group $$K$$ and a normal subgroup $$N$$ of $$K$$ such that $$G$$ is isomorphic to the quotient group $$K/N$$.

Facts used

 * 1) uses::Every group is a quotient of a free group
 * 2) uses::Free implies residually finite

Proof
The proof follows directly by combining Facts (1) and (2). More explicitly, we choose the residually finite group to be the free group arising in the proof of Fact (1).