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\begin{array}{l}\phantom{59)}\phantom{1}\\59\overline{)59}\\\end{array}
Use the 1^{st} digit 5 from dividend 59
\begin{array}{l}\phantom{59)}0\phantom{2}\\59\overline{)59}\\\end{array}
Since 5 is less than 59, use the next digit 9 from dividend 59 and add 0 to the quotient
\begin{array}{l}\phantom{59)}0\phantom{3}\\59\overline{)59}\\\end{array}
Use the 2^{nd} digit 9 from dividend 59
\begin{array}{l}\phantom{59)}01\phantom{4}\\59\overline{)59}\\\phantom{59)}\underline{\phantom{}59\phantom{}}\\\phantom{59)99}0\\\end{array}
Find closest multiple of 59 to 59. We see that 1 \times 59 = 59 is the nearest. Now subtract 59 from 59 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }0
Since 0 is less than 59, stop the division. The reminder is 0. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.