What is 684 divided by 57?

57 goes into 68 one time ($1 \times 57 = 57$). Write 1 in the quotient above the 8.
Subtract 57 from 68.

$$\begin{array}{r} 1\phantom{0} \\ 57\overline{\smash{)}684} \\ -57\downarrow \\ \hline 11\phantom{0} \\ \end{array}$$

$68 - 57 = 11$.

Divide 114 by 57.
57 goes into 114 two times ($2 \times 57 = 114$). Write 2 in the quotient above the 4.
Subtract 114 from 114.

$$\begin{array}{r} 12 \\ 57\overline{\smash{)}684} \\ -57\downarrow \\ \hline 114 \\ -114 \\ \hline 0 \\ \end{array}$$

$114 - 114 = 0$.

The quotient is 12.

$$684 \div 57 = \boxed{\text{12}}$$