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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)581}\\\end{array}
Use the 1^{st} digit 5 from dividend 581
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)581}\\\end{array}
Since 5 is less than 100, use the next digit 8 from dividend 581 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)581}\\\end{array}
Use the 2^{nd} digit 8 from dividend 581
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)581}\\\end{array}
Since 58 is less than 100, use the next digit 1 from dividend 581 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)581}\\\end{array}
Use the 3^{rd} digit 1 from dividend 581
\begin{array}{l}\phantom{100)}005\phantom{6}\\100\overline{)581}\\\phantom{100)}\underline{\phantom{}500\phantom{}}\\\phantom{100)9}81\\\end{array}
Find closest multiple of 100 to 581. We see that 5 \times 100 = 500 is the nearest. Now subtract 500 from 581 to get reminder 81. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }81
Since 81 is less than 100, stop the division. The reminder is 81. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.