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\begin{array}{l}\phantom{125)}\phantom{1}\\125\overline{)4375}\\\end{array}
Use the 1^{st} digit 4 from dividend 4375
\begin{array}{l}\phantom{125)}0\phantom{2}\\125\overline{)4375}\\\end{array}
Since 4 is less than 125, use the next digit 3 from dividend 4375 and add 0 to the quotient
\begin{array}{l}\phantom{125)}0\phantom{3}\\125\overline{)4375}\\\end{array}
Use the 2^{nd} digit 3 from dividend 4375
\begin{array}{l}\phantom{125)}00\phantom{4}\\125\overline{)4375}\\\end{array}
Since 43 is less than 125, use the next digit 7 from dividend 4375 and add 0 to the quotient
\begin{array}{l}\phantom{125)}00\phantom{5}\\125\overline{)4375}\\\end{array}
Use the 3^{rd} digit 7 from dividend 4375
\begin{array}{l}\phantom{125)}003\phantom{6}\\125\overline{)4375}\\\phantom{125)}\underline{\phantom{}375\phantom{9}}\\\phantom{125)9}62\\\end{array}
Find closest multiple of 125 to 437. We see that 3 \times 125 = 375 is the nearest. Now subtract 375 from 437 to get reminder 62. Add 3 to quotient.
\begin{array}{l}\phantom{125)}003\phantom{7}\\125\overline{)4375}\\\phantom{125)}\underline{\phantom{}375\phantom{9}}\\\phantom{125)9}625\\\end{array}
Use the 4^{th} digit 5 from dividend 4375
\begin{array}{l}\phantom{125)}0035\phantom{8}\\125\overline{)4375}\\\phantom{125)}\underline{\phantom{}375\phantom{9}}\\\phantom{125)9}625\\\phantom{125)}\underline{\phantom{9}625\phantom{}}\\\phantom{125)9999}0\\\end{array}
Find closest multiple of 125 to 625. We see that 5 \times 125 = 625 is the nearest. Now subtract 625 from 625 to get reminder 0. Add 5 to quotient.
\text{Quotient: }35 \text{Reminder: }0
Since 0 is less than 125, 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.