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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)52}\\\end{array}
Use the 1^{st} digit 5 from dividend 52
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)52}\\\end{array}
Since 5 is less than 13, use the next digit 2 from dividend 52 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)52}\\\end{array}
Use the 2^{nd} digit 2 from dividend 52
\begin{array}{l}\phantom{13)}04\phantom{4}\\13\overline{)52}\\\phantom{13)}\underline{\phantom{}52\phantom{}}\\\phantom{13)99}0\\\end{array}
Find closest multiple of 13 to 52. We see that 4 \times 13 = 52 is the nearest. Now subtract 52 from 52 to get reminder 0. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }0
Since 0 is less than 13, stop the division. The reminder is 0. The topmost line 04 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.