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\begin{array}{l}\phantom{55)}\phantom{1}\\55\overline{)605}\\\end{array}
Use the 1^{st} digit 6 from dividend 605
\begin{array}{l}\phantom{55)}0\phantom{2}\\55\overline{)605}\\\end{array}
Since 6 is less than 55, use the next digit 0 from dividend 605 and add 0 to the quotient
\begin{array}{l}\phantom{55)}0\phantom{3}\\55\overline{)605}\\\end{array}
Use the 2^{nd} digit 0 from dividend 605
\begin{array}{l}\phantom{55)}01\phantom{4}\\55\overline{)605}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)9}5\\\end{array}
Find closest multiple of 55 to 60. We see that 1 \times 55 = 55 is the nearest. Now subtract 55 from 60 to get reminder 5. Add 1 to quotient.
\begin{array}{l}\phantom{55)}01\phantom{5}\\55\overline{)605}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)9}55\\\end{array}
Use the 3^{rd} digit 5 from dividend 605
\begin{array}{l}\phantom{55)}011\phantom{6}\\55\overline{)605}\\\phantom{55)}\underline{\phantom{}55\phantom{9}}\\\phantom{55)9}55\\\phantom{55)}\underline{\phantom{9}55\phantom{}}\\\phantom{55)999}0\\\end{array}
Find closest multiple of 55 to 55. We see that 1 \times 55 = 55 is the nearest. Now subtract 55 from 55 to get reminder 0. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }0
Since 0 is less than 55, stop the division. The reminder is 0. The topmost line 011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.