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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)91}\\\end{array}
Use the 1^{st} digit 9 from dividend 91
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)91}\\\end{array}
Since 9 is less than 13, use the next digit 1 from dividend 91 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)91}\\\end{array}
Use the 2^{nd} digit 1 from dividend 91
\begin{array}{l}\phantom{13)}07\phantom{4}\\13\overline{)91}\\\phantom{13)}\underline{\phantom{}91\phantom{}}\\\phantom{13)99}0\\\end{array}
Find closest multiple of 13 to 91. We see that 7 \times 13 = 91 is the nearest. Now subtract 91 from 91 to get reminder 0. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }0
Since 0 is less than 13, stop the division. The reminder is 0. The topmost line 07 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.