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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)44}\\\end{array}
Use the 1^{st} digit 4 from dividend 44
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)44}\\\end{array}
Since 4 is less than 15, use the next digit 4 from dividend 44 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)44}\\\end{array}
Use the 2^{nd} digit 4 from dividend 44
\begin{array}{l}\phantom{15)}02\phantom{4}\\15\overline{)44}\\\phantom{15)}\underline{\phantom{}30\phantom{}}\\\phantom{15)}14\\\end{array}
Find closest multiple of 15 to 44. We see that 2 \times 15 = 30 is the nearest. Now subtract 30 from 44 to get reminder 14. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }14
Since 14 is less than 15, stop the division. The reminder is 14. The topmost line 02 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.