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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)450}\\\end{array}
Use the 1^{st} digit 4 from dividend 450
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)450}\\\end{array}
Since 4 is less than 13, use the next digit 5 from dividend 450 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)450}\\\end{array}
Use the 2^{nd} digit 5 from dividend 450
\begin{array}{l}\phantom{13)}03\phantom{4}\\13\overline{)450}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}6\\\end{array}
Find closest multiple of 13 to 45. We see that 3 \times 13 = 39 is the nearest. Now subtract 39 from 45 to get reminder 6. Add 3 to quotient.
\begin{array}{l}\phantom{13)}03\phantom{5}\\13\overline{)450}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}60\\\end{array}
Use the 3^{rd} digit 0 from dividend 450
\begin{array}{l}\phantom{13)}034\phantom{6}\\13\overline{)450}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}60\\\phantom{13)}\underline{\phantom{9}52\phantom{}}\\\phantom{13)99}8\\\end{array}
Find closest multiple of 13 to 60. We see that 4 \times 13 = 52 is the nearest. Now subtract 52 from 60 to get reminder 8. Add 4 to quotient.
\text{Quotient: }34 \text{Reminder: }8
Since 8 is less than 13, stop the division. The reminder is 8. The topmost line 034 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 34.