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\begin{array}{l}\phantom{555)}\phantom{1}\\555\overline{)999}\\\end{array}
Use the 1^{st} digit 9 from dividend 999
\begin{array}{l}\phantom{555)}0\phantom{2}\\555\overline{)999}\\\end{array}
Since 9 is less than 555, use the next digit 9 from dividend 999 and add 0 to the quotient
\begin{array}{l}\phantom{555)}0\phantom{3}\\555\overline{)999}\\\end{array}
Use the 2^{nd} digit 9 from dividend 999
\begin{array}{l}\phantom{555)}00\phantom{4}\\555\overline{)999}\\\end{array}
Since 99 is less than 555, use the next digit 9 from dividend 999 and add 0 to the quotient
\begin{array}{l}\phantom{555)}00\phantom{5}\\555\overline{)999}\\\end{array}
Use the 3^{rd} digit 9 from dividend 999
\begin{array}{l}\phantom{555)}001\phantom{6}\\555\overline{)999}\\\phantom{555)}\underline{\phantom{}555\phantom{}}\\\phantom{555)}444\\\end{array}
Find closest multiple of 555 to 999. We see that 1 \times 555 = 555 is the nearest. Now subtract 555 from 999 to get reminder 444. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }444
Since 444 is less than 555, stop the division. The reminder is 444. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.