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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)80}\\\end{array}
Use the 1^{st} digit 8 from dividend 80
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)80}\\\end{array}
Since 8 is less than 35, use the next digit 0 from dividend 80 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)80}\\\end{array}
Use the 2^{nd} digit 0 from dividend 80
\begin{array}{l}\phantom{35)}02\phantom{4}\\35\overline{)80}\\\phantom{35)}\underline{\phantom{}70\phantom{}}\\\phantom{35)}10\\\end{array}
Find closest multiple of 35 to 80. We see that 2 \times 35 = 70 is the nearest. Now subtract 70 from 80 to get reminder 10. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }10
Since 10 is less than 35, stop the division. The reminder is 10. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.