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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)377}\\\end{array}
Use the 1^{st} digit 3 from dividend 377
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)377}\\\end{array}
Since 3 is less than 60, use the next digit 7 from dividend 377 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)377}\\\end{array}
Use the 2^{nd} digit 7 from dividend 377
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)377}\\\end{array}
Since 37 is less than 60, use the next digit 7 from dividend 377 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)377}\\\end{array}
Use the 3^{rd} digit 7 from dividend 377
\begin{array}{l}\phantom{60)}006\phantom{6}\\60\overline{)377}\\\phantom{60)}\underline{\phantom{}360\phantom{}}\\\phantom{60)9}17\\\end{array}
Find closest multiple of 60 to 377. We see that 6 \times 60 = 360 is the nearest. Now subtract 360 from 377 to get reminder 17. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }17
Since 17 is less than 60, stop the division. The reminder is 17. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.