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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)306}\\\end{array}
Use the 1^{st} digit 3 from dividend 306
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)306}\\\end{array}
Since 3 is less than 45, use the next digit 0 from dividend 306 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)306}\\\end{array}
Use the 2^{nd} digit 0 from dividend 306
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)306}\\\end{array}
Since 30 is less than 45, use the next digit 6 from dividend 306 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)306}\\\end{array}
Use the 3^{rd} digit 6 from dividend 306
\begin{array}{l}\phantom{45)}006\phantom{6}\\45\overline{)306}\\\phantom{45)}\underline{\phantom{}270\phantom{}}\\\phantom{45)9}36\\\end{array}
Find closest multiple of 45 to 306. We see that 6 \times 45 = 270 is the nearest. Now subtract 270 from 306 to get reminder 36. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }36
Since 36 is less than 45, stop the division. The reminder is 36. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.