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\begin{array}{l}\phantom{59)}\phantom{1}\\59\overline{)555}\\\end{array}
Use the 1^{st} digit 5 from dividend 555
\begin{array}{l}\phantom{59)}0\phantom{2}\\59\overline{)555}\\\end{array}
Since 5 is less than 59, use the next digit 5 from dividend 555 and add 0 to the quotient
\begin{array}{l}\phantom{59)}0\phantom{3}\\59\overline{)555}\\\end{array}
Use the 2^{nd} digit 5 from dividend 555
\begin{array}{l}\phantom{59)}00\phantom{4}\\59\overline{)555}\\\end{array}
Since 55 is less than 59, use the next digit 5 from dividend 555 and add 0 to the quotient
\begin{array}{l}\phantom{59)}00\phantom{5}\\59\overline{)555}\\\end{array}
Use the 3^{rd} digit 5 from dividend 555
\begin{array}{l}\phantom{59)}009\phantom{6}\\59\overline{)555}\\\phantom{59)}\underline{\phantom{}531\phantom{}}\\\phantom{59)9}24\\\end{array}
Find closest multiple of 59 to 555. We see that 9 \times 59 = 531 is the nearest. Now subtract 531 from 555 to get reminder 24. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }24
Since 24 is less than 59, stop the division. The reminder is 24. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.