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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)60}\\\end{array}
Use the 1^{st} digit 6 from dividend 60
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)60}\\\end{array}
Since 6 is less than 60, use the next digit 0 from dividend 60 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)60}\\\end{array}
Use the 2^{nd} digit 0 from dividend 60
\begin{array}{l}\phantom{60)}01\phantom{4}\\60\overline{)60}\\\phantom{60)}\underline{\phantom{}60\phantom{}}\\\phantom{60)99}0\\\end{array}
Find closest multiple of 60 to 60. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 60 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }0
Since 0 is less than 60, 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.