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\begin{array}{l}\phantom{144)}\phantom{1}\\144\overline{)1296}\\\end{array}
Use the 1^{st} digit 1 from dividend 1296
\begin{array}{l}\phantom{144)}0\phantom{2}\\144\overline{)1296}\\\end{array}
Since 1 is less than 144, use the next digit 2 from dividend 1296 and add 0 to the quotient
\begin{array}{l}\phantom{144)}0\phantom{3}\\144\overline{)1296}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1296
\begin{array}{l}\phantom{144)}00\phantom{4}\\144\overline{)1296}\\\end{array}
Since 12 is less than 144, use the next digit 9 from dividend 1296 and add 0 to the quotient
\begin{array}{l}\phantom{144)}00\phantom{5}\\144\overline{)1296}\\\end{array}
Use the 3^{rd} digit 9 from dividend 1296
\begin{array}{l}\phantom{144)}000\phantom{6}\\144\overline{)1296}\\\end{array}
Since 129 is less than 144, use the next digit 6 from dividend 1296 and add 0 to the quotient
\begin{array}{l}\phantom{144)}000\phantom{7}\\144\overline{)1296}\\\end{array}
Use the 4^{th} digit 6 from dividend 1296
\begin{array}{l}\phantom{144)}0009\phantom{8}\\144\overline{)1296}\\\phantom{144)}\underline{\phantom{}1296\phantom{}}\\\phantom{144)9999}0\\\end{array}
Find closest multiple of 144 to 1296. We see that 9 \times 144 = 1296 is the nearest. Now subtract 1296 from 1296 to get reminder 0. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }0
Since 0 is less than 144, stop the division. The reminder is 0. The topmost line 0009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.