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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)1900}\\\end{array}
Use the 1^{st} digit 1 from dividend 1900
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)1900}\\\end{array}
Since 1 is less than 100, use the next digit 9 from dividend 1900 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)1900}\\\end{array}
Use the 2^{nd} digit 9 from dividend 1900
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)1900}\\\end{array}
Since 19 is less than 100, use the next digit 0 from dividend 1900 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)1900}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1900
\begin{array}{l}\phantom{100)}001\phantom{6}\\100\overline{)1900}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}90\\\end{array}
Find closest multiple of 100 to 190. We see that 1 \times 100 = 100 is the nearest. Now subtract 100 from 190 to get reminder 90. Add 1 to quotient.
\begin{array}{l}\phantom{100)}001\phantom{7}\\100\overline{)1900}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}900\\\end{array}
Use the 4^{th} digit 0 from dividend 1900
\begin{array}{l}\phantom{100)}0019\phantom{8}\\100\overline{)1900}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}900\\\phantom{100)}\underline{\phantom{9}900\phantom{}}\\\phantom{100)9999}0\\\end{array}
Find closest multiple of 100 to 900. We see that 9 \times 100 = 900 is the nearest. Now subtract 900 from 900 to get reminder 0. Add 9 to quotient.
\text{Quotient: }19 \text{Reminder: }0
Since 0 is less than 100, stop the division. The reminder is 0. The topmost line 0019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.