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\begin{array}{l}\phantom{625)}\phantom{1}\\625\overline{)684}\\\end{array}
Use the 1^{st} digit 6 from dividend 684
\begin{array}{l}\phantom{625)}0\phantom{2}\\625\overline{)684}\\\end{array}
Since 6 is less than 625, use the next digit 8 from dividend 684 and add 0 to the quotient
\begin{array}{l}\phantom{625)}0\phantom{3}\\625\overline{)684}\\\end{array}
Use the 2^{nd} digit 8 from dividend 684
\begin{array}{l}\phantom{625)}00\phantom{4}\\625\overline{)684}\\\end{array}
Since 68 is less than 625, use the next digit 4 from dividend 684 and add 0 to the quotient
\begin{array}{l}\phantom{625)}00\phantom{5}\\625\overline{)684}\\\end{array}
Use the 3^{rd} digit 4 from dividend 684
\begin{array}{l}\phantom{625)}001\phantom{6}\\625\overline{)684}\\\phantom{625)}\underline{\phantom{}625\phantom{}}\\\phantom{625)9}59\\\end{array}
Find closest multiple of 625 to 684. We see that 1 \times 625 = 625 is the nearest. Now subtract 625 from 684 to get reminder 59. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }59
Since 59 is less than 625, stop the division. The reminder is 59. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.