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\begin{array}{l}\phantom{300)}\phantom{1}\\300\overline{)600}\\\end{array}
Use the 1^{st} digit 6 from dividend 600
\begin{array}{l}\phantom{300)}0\phantom{2}\\300\overline{)600}\\\end{array}
Since 6 is less than 300, use the next digit 0 from dividend 600 and add 0 to the quotient
\begin{array}{l}\phantom{300)}0\phantom{3}\\300\overline{)600}\\\end{array}
Use the 2^{nd} digit 0 from dividend 600
\begin{array}{l}\phantom{300)}00\phantom{4}\\300\overline{)600}\\\end{array}
Since 60 is less than 300, use the next digit 0 from dividend 600 and add 0 to the quotient
\begin{array}{l}\phantom{300)}00\phantom{5}\\300\overline{)600}\\\end{array}
Use the 3^{rd} digit 0 from dividend 600
\begin{array}{l}\phantom{300)}002\phantom{6}\\300\overline{)600}\\\phantom{300)}\underline{\phantom{}600\phantom{}}\\\phantom{300)999}0\\\end{array}
Find closest multiple of 300 to 600. We see that 2 \times 300 = 600 is the nearest. Now subtract 600 from 600 to get reminder 0. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }0
Since 0 is less than 300, stop the division. The reminder is 0. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.