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\begin{array}{l}\phantom{16)}\phantom{1}\\16\overline{)588}\\\end{array}
Use the 1^{st} digit 5 from dividend 588
\begin{array}{l}\phantom{16)}0\phantom{2}\\16\overline{)588}\\\end{array}
Since 5 is less than 16, use the next digit 8 from dividend 588 and add 0 to the quotient
\begin{array}{l}\phantom{16)}0\phantom{3}\\16\overline{)588}\\\end{array}
Use the 2^{nd} digit 8 from dividend 588
\begin{array}{l}\phantom{16)}03\phantom{4}\\16\overline{)588}\\\phantom{16)}\underline{\phantom{}48\phantom{9}}\\\phantom{16)}10\\\end{array}
Find closest multiple of 16 to 58. We see that 3 \times 16 = 48 is the nearest. Now subtract 48 from 58 to get reminder 10. Add 3 to quotient.
\begin{array}{l}\phantom{16)}03\phantom{5}\\16\overline{)588}\\\phantom{16)}\underline{\phantom{}48\phantom{9}}\\\phantom{16)}108\\\end{array}
Use the 3^{rd} digit 8 from dividend 588
\begin{array}{l}\phantom{16)}036\phantom{6}\\16\overline{)588}\\\phantom{16)}\underline{\phantom{}48\phantom{9}}\\\phantom{16)}108\\\phantom{16)}\underline{\phantom{9}96\phantom{}}\\\phantom{16)9}12\\\end{array}
Find closest multiple of 16 to 108. We see that 6 \times 16 = 96 is the nearest. Now subtract 96 from 108 to get reminder 12. Add 6 to quotient.
\text{Quotient: }36 \text{Reminder: }12
Since 12 is less than 16, stop the division. The reminder is 12. The topmost line 036 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 36.