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\begin{array}{l}\phantom{38)}\phantom{1}\\38\overline{)304}\\\end{array}
Use the 1^{st} digit 3 from dividend 304
\begin{array}{l}\phantom{38)}0\phantom{2}\\38\overline{)304}\\\end{array}
Since 3 is less than 38, use the next digit 0 from dividend 304 and add 0 to the quotient
\begin{array}{l}\phantom{38)}0\phantom{3}\\38\overline{)304}\\\end{array}
Use the 2^{nd} digit 0 from dividend 304
\begin{array}{l}\phantom{38)}00\phantom{4}\\38\overline{)304}\\\end{array}
Since 30 is less than 38, use the next digit 4 from dividend 304 and add 0 to the quotient
\begin{array}{l}\phantom{38)}00\phantom{5}\\38\overline{)304}\\\end{array}
Use the 3^{rd} digit 4 from dividend 304
\begin{array}{l}\phantom{38)}008\phantom{6}\\38\overline{)304}\\\phantom{38)}\underline{\phantom{}304\phantom{}}\\\phantom{38)999}0\\\end{array}
Find closest multiple of 38 to 304. We see that 8 \times 38 = 304 is the nearest. Now subtract 304 from 304 to get reminder 0. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }0
Since 0 is less than 38, 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.