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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)4100}\\\end{array}
Use the 1^{st} digit 4 from dividend 4100
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)4100}\\\end{array}
Since 4 is less than 100, use the next digit 1 from dividend 4100 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)4100}\\\end{array}
Use the 2^{nd} digit 1 from dividend 4100
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)4100}\\\end{array}
Since 41 is less than 100, use the next digit 0 from dividend 4100 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)4100}\\\end{array}
Use the 3^{rd} digit 0 from dividend 4100
\begin{array}{l}\phantom{100)}004\phantom{6}\\100\overline{)4100}\\\phantom{100)}\underline{\phantom{}400\phantom{9}}\\\phantom{100)9}10\\\end{array}
Find closest multiple of 100 to 410. We see that 4 \times 100 = 400 is the nearest. Now subtract 400 from 410 to get reminder 10. Add 4 to quotient.
\begin{array}{l}\phantom{100)}004\phantom{7}\\100\overline{)4100}\\\phantom{100)}\underline{\phantom{}400\phantom{9}}\\\phantom{100)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 4100
\begin{array}{l}\phantom{100)}0041\phantom{8}\\100\overline{)4100}\\\phantom{100)}\underline{\phantom{}400\phantom{9}}\\\phantom{100)9}100\\\phantom{100)}\underline{\phantom{9}100\phantom{}}\\\phantom{100)9999}0\\\end{array}
Find closest multiple of 100 to 100. We see that 1 \times 100 = 100 is the nearest. Now subtract 100 from 100 to get reminder 0. Add 1 to quotient.
\text{Quotient: }41 \text{Reminder: }0
Since 0 is less than 100, stop the division. The reminder is 0. The topmost line 0041 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 41.