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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)631}\\\end{array}
Use the 1^{st} digit 6 from dividend 631
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)631}\\\end{array}
Since 6 is less than 100, use the next digit 3 from dividend 631 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)631}\\\end{array}
Use the 2^{nd} digit 3 from dividend 631
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)631}\\\end{array}
Since 63 is less than 100, use the next digit 1 from dividend 631 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)631}\\\end{array}
Use the 3^{rd} digit 1 from dividend 631
\begin{array}{l}\phantom{100)}006\phantom{6}\\100\overline{)631}\\\phantom{100)}\underline{\phantom{}600\phantom{}}\\\phantom{100)9}31\\\end{array}
Find closest multiple of 100 to 631. We see that 6 \times 100 = 600 is the nearest. Now subtract 600 from 631 to get reminder 31. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }31
Since 31 is less than 100, stop the division. The reminder is 31. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.