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\begin{array}{l}\phantom{120)}\phantom{1}\\120\overline{)4200}\\\end{array}
Use the 1^{st} digit 4 from dividend 4200
\begin{array}{l}\phantom{120)}0\phantom{2}\\120\overline{)4200}\\\end{array}
Since 4 is less than 120, use the next digit 2 from dividend 4200 and add 0 to the quotient
\begin{array}{l}\phantom{120)}0\phantom{3}\\120\overline{)4200}\\\end{array}
Use the 2^{nd} digit 2 from dividend 4200
\begin{array}{l}\phantom{120)}00\phantom{4}\\120\overline{)4200}\\\end{array}
Since 42 is less than 120, use the next digit 0 from dividend 4200 and add 0 to the quotient
\begin{array}{l}\phantom{120)}00\phantom{5}\\120\overline{)4200}\\\end{array}
Use the 3^{rd} digit 0 from dividend 4200
\begin{array}{l}\phantom{120)}003\phantom{6}\\120\overline{)4200}\\\phantom{120)}\underline{\phantom{}360\phantom{9}}\\\phantom{120)9}60\\\end{array}
Find closest multiple of 120 to 420. We see that 3 \times 120 = 360 is the nearest. Now subtract 360 from 420 to get reminder 60. Add 3 to quotient.
\begin{array}{l}\phantom{120)}003\phantom{7}\\120\overline{)4200}\\\phantom{120)}\underline{\phantom{}360\phantom{9}}\\\phantom{120)9}600\\\end{array}
Use the 4^{th} digit 0 from dividend 4200
\begin{array}{l}\phantom{120)}0035\phantom{8}\\120\overline{)4200}\\\phantom{120)}\underline{\phantom{}360\phantom{9}}\\\phantom{120)9}600\\\phantom{120)}\underline{\phantom{9}600\phantom{}}\\\phantom{120)9999}0\\\end{array}
Find closest multiple of 120 to 600. We see that 5 \times 120 = 600 is the nearest. Now subtract 600 from 600 to get reminder 0. Add 5 to quotient.
\text{Quotient: }35 \text{Reminder: }0
Since 0 is less than 120, stop the division. The reminder is 0. The topmost line 0035 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 35.