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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)27}\\\end{array}
Use the 1^{st} digit 2 from dividend 27
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)27}\\\end{array}
Since 2 is less than 13, use the next digit 7 from dividend 27 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)27}\\\end{array}
Use the 2^{nd} digit 7 from dividend 27
\begin{array}{l}\phantom{13)}02\phantom{4}\\13\overline{)27}\\\phantom{13)}\underline{\phantom{}26\phantom{}}\\\phantom{13)9}1\\\end{array}
Find closest multiple of 13 to 27. We see that 2 \times 13 = 26 is the nearest. Now subtract 26 from 27 to get reminder 1. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }1
Since 1 is less than 13, stop the division. The reminder is 1. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.