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\begin{array}{l}\phantom{1080)}\phantom{1}\\1080\overline{)1728}\\\end{array}
Use the 1^{st} digit 1 from dividend 1728
\begin{array}{l}\phantom{1080)}0\phantom{2}\\1080\overline{)1728}\\\end{array}
Since 1 is less than 1080, use the next digit 7 from dividend 1728 and add 0 to the quotient
\begin{array}{l}\phantom{1080)}0\phantom{3}\\1080\overline{)1728}\\\end{array}
Use the 2^{nd} digit 7 from dividend 1728
\begin{array}{l}\phantom{1080)}00\phantom{4}\\1080\overline{)1728}\\\end{array}
Since 17 is less than 1080, use the next digit 2 from dividend 1728 and add 0 to the quotient
\begin{array}{l}\phantom{1080)}00\phantom{5}\\1080\overline{)1728}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1728
\begin{array}{l}\phantom{1080)}000\phantom{6}\\1080\overline{)1728}\\\end{array}
Since 172 is less than 1080, use the next digit 8 from dividend 1728 and add 0 to the quotient
\begin{array}{l}\phantom{1080)}000\phantom{7}\\1080\overline{)1728}\\\end{array}
Use the 4^{th} digit 8 from dividend 1728
\begin{array}{l}\phantom{1080)}0001\phantom{8}\\1080\overline{)1728}\\\phantom{1080)}\underline{\phantom{}1080\phantom{}}\\\phantom{1080)9}648\\\end{array}
Find closest multiple of 1080 to 1728. We see that 1 \times 1080 = 1080 is the nearest. Now subtract 1080 from 1728 to get reminder 648. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }648
Since 648 is less than 1080, stop the division. The reminder is 648. The topmost line 0001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.