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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)89}\\\end{array}
Use the 1^{st} digit 8 from dividend 89
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)89}\\\end{array}
Since 8 is less than 13, use the next digit 9 from dividend 89 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)89}\\\end{array}
Use the 2^{nd} digit 9 from dividend 89
\begin{array}{l}\phantom{13)}06\phantom{4}\\13\overline{)89}\\\phantom{13)}\underline{\phantom{}78\phantom{}}\\\phantom{13)}11\\\end{array}
Find closest multiple of 13 to 89. We see that 6 \times 13 = 78 is the nearest. Now subtract 78 from 89 to get reminder 11. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }11
Since 11 is less than 13, stop the division. The reminder is 11. The topmost line 06 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.