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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)345}\\\end{array}
Use the 1^{st} digit 3 from dividend 345
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)345}\\\end{array}
Since 3 is less than 100, use the next digit 4 from dividend 345 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)345}\\\end{array}
Use the 2^{nd} digit 4 from dividend 345
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)345}\\\end{array}
Since 34 is less than 100, use the next digit 5 from dividend 345 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)345}\\\end{array}
Use the 3^{rd} digit 5 from dividend 345
\begin{array}{l}\phantom{100)}003\phantom{6}\\100\overline{)345}\\\phantom{100)}\underline{\phantom{}300\phantom{}}\\\phantom{100)9}45\\\end{array}
Find closest multiple of 100 to 345. We see that 3 \times 100 = 300 is the nearest. Now subtract 300 from 345 to get reminder 45. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }45
Since 45 is less than 100, stop the division. The reminder is 45. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.