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\begin{array}{l}\phantom{76)}\phantom{1}\\76\overline{)608}\\\end{array}
Use the 1^{st} digit 6 from dividend 608
\begin{array}{l}\phantom{76)}0\phantom{2}\\76\overline{)608}\\\end{array}
Since 6 is less than 76, use the next digit 0 from dividend 608 and add 0 to the quotient
\begin{array}{l}\phantom{76)}0\phantom{3}\\76\overline{)608}\\\end{array}
Use the 2^{nd} digit 0 from dividend 608
\begin{array}{l}\phantom{76)}00\phantom{4}\\76\overline{)608}\\\end{array}
Since 60 is less than 76, use the next digit 8 from dividend 608 and add 0 to the quotient
\begin{array}{l}\phantom{76)}00\phantom{5}\\76\overline{)608}\\\end{array}
Use the 3^{rd} digit 8 from dividend 608
\begin{array}{l}\phantom{76)}008\phantom{6}\\76\overline{)608}\\\phantom{76)}\underline{\phantom{}608\phantom{}}\\\phantom{76)999}0\\\end{array}
Find closest multiple of 76 to 608. We see that 8 \times 76 = 608 is the nearest. Now subtract 608 from 608 to get reminder 0. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }0
Since 0 is less than 76, stop the division. The reminder is 0. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.