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\begin{array}{l}\phantom{300)}\phantom{1}\\300\overline{)855}\\\end{array}
Use the 1^{st} digit 8 from dividend 855
\begin{array}{l}\phantom{300)}0\phantom{2}\\300\overline{)855}\\\end{array}
Since 8 is less than 300, use the next digit 5 from dividend 855 and add 0 to the quotient
\begin{array}{l}\phantom{300)}0\phantom{3}\\300\overline{)855}\\\end{array}
Use the 2^{nd} digit 5 from dividend 855
\begin{array}{l}\phantom{300)}00\phantom{4}\\300\overline{)855}\\\end{array}
Since 85 is less than 300, use the next digit 5 from dividend 855 and add 0 to the quotient
\begin{array}{l}\phantom{300)}00\phantom{5}\\300\overline{)855}\\\end{array}
Use the 3^{rd} digit 5 from dividend 855
\begin{array}{l}\phantom{300)}002\phantom{6}\\300\overline{)855}\\\phantom{300)}\underline{\phantom{}600\phantom{}}\\\phantom{300)}255\\\end{array}
Find closest multiple of 300 to 855. We see that 2 \times 300 = 600 is the nearest. Now subtract 600 from 855 to get reminder 255. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }255
Since 255 is less than 300, stop the division. The reminder is 255. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.