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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)507}\\\end{array}
Use the 1^{st} digit 5 from dividend 507
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)507}\\\end{array}
Since 5 is less than 13, use the next digit 0 from dividend 507 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)507}\\\end{array}
Use the 2^{nd} digit 0 from dividend 507
\begin{array}{l}\phantom{13)}03\phantom{4}\\13\overline{)507}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)}11\\\end{array}
Find closest multiple of 13 to 50. We see that 3 \times 13 = 39 is the nearest. Now subtract 39 from 50 to get reminder 11. Add 3 to quotient.
\begin{array}{l}\phantom{13)}03\phantom{5}\\13\overline{)507}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)}117\\\end{array}
Use the 3^{rd} digit 7 from dividend 507
\begin{array}{l}\phantom{13)}039\phantom{6}\\13\overline{)507}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)}117\\\phantom{13)}\underline{\phantom{}117\phantom{}}\\\phantom{13)999}0\\\end{array}
Find closest multiple of 13 to 117. We see that 9 \times 13 = 117 is the nearest. Now subtract 117 from 117 to get reminder 0. Add 9 to quotient.
\text{Quotient: }39 \text{Reminder: }0
Since 0 is less than 13, stop the division. The reminder is 0. The topmost line 039 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 39.