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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)88}\\\end{array}
Use the 1^{st} digit 8 from dividend 88
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)88}\\\end{array}
Since 8 is less than 13, use the next digit 8 from dividend 88 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)88}\\\end{array}
Use the 2^{nd} digit 8 from dividend 88
\begin{array}{l}\phantom{13)}06\phantom{4}\\13\overline{)88}\\\phantom{13)}\underline{\phantom{}78\phantom{}}\\\phantom{13)}10\\\end{array}
Find closest multiple of 13 to 88. We see that 6 \times 13 = 78 is the nearest. Now subtract 78 from 88 to get reminder 10. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }10
Since 10 is less than 13, stop the division. The reminder is 10. The topmost line 06 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.