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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)5577}\\\end{array}
Use the 1^{st} digit 5 from dividend 5577
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)5577}\\\end{array}
Since 5 is less than 100, use the next digit 5 from dividend 5577 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)5577}\\\end{array}
Use the 2^{nd} digit 5 from dividend 5577
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)5577}\\\end{array}
Since 55 is less than 100, use the next digit 7 from dividend 5577 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)5577}\\\end{array}
Use the 3^{rd} digit 7 from dividend 5577
\begin{array}{l}\phantom{100)}005\phantom{6}\\100\overline{)5577}\\\phantom{100)}\underline{\phantom{}500\phantom{9}}\\\phantom{100)9}57\\\end{array}
Find closest multiple of 100 to 557. We see that 5 \times 100 = 500 is the nearest. Now subtract 500 from 557 to get reminder 57. Add 5 to quotient.
\begin{array}{l}\phantom{100)}005\phantom{7}\\100\overline{)5577}\\\phantom{100)}\underline{\phantom{}500\phantom{9}}\\\phantom{100)9}577\\\end{array}
Use the 4^{th} digit 7 from dividend 5577
\begin{array}{l}\phantom{100)}0055\phantom{8}\\100\overline{)5577}\\\phantom{100)}\underline{\phantom{}500\phantom{9}}\\\phantom{100)9}577\\\phantom{100)}\underline{\phantom{9}500\phantom{}}\\\phantom{100)99}77\\\end{array}
Find closest multiple of 100 to 577. We see that 5 \times 100 = 500 is the nearest. Now subtract 500 from 577 to get reminder 77. Add 5 to quotient.
\text{Quotient: }55 \text{Reminder: }77
Since 77 is less than 100, stop the division. The reminder is 77. The topmost line 0055 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 55.