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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)839}\\\end{array}
Use the 1^{st} digit 8 from dividend 839
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)839}\\\end{array}
Since 8 is less than 13, use the next digit 3 from dividend 839 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)839}\\\end{array}
Use the 2^{nd} digit 3 from dividend 839
\begin{array}{l}\phantom{13)}06\phantom{4}\\13\overline{)839}\\\phantom{13)}\underline{\phantom{}78\phantom{9}}\\\phantom{13)9}5\\\end{array}
Find closest multiple of 13 to 83. We see that 6 \times 13 = 78 is the nearest. Now subtract 78 from 83 to get reminder 5. Add 6 to quotient.
\begin{array}{l}\phantom{13)}06\phantom{5}\\13\overline{)839}\\\phantom{13)}\underline{\phantom{}78\phantom{9}}\\\phantom{13)9}59\\\end{array}
Use the 3^{rd} digit 9 from dividend 839
\begin{array}{l}\phantom{13)}064\phantom{6}\\13\overline{)839}\\\phantom{13)}\underline{\phantom{}78\phantom{9}}\\\phantom{13)9}59\\\phantom{13)}\underline{\phantom{9}52\phantom{}}\\\phantom{13)99}7\\\end{array}
Find closest multiple of 13 to 59. We see that 4 \times 13 = 52 is the nearest. Now subtract 52 from 59 to get reminder 7. Add 4 to quotient.
\text{Quotient: }64 \text{Reminder: }7
Since 7 is less than 13, stop the division. The reminder is 7. The topmost line 064 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 64.