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\begin{array}{l}\phantom{44)}\phantom{1}\\44\overline{)44}\\\end{array}
Use the 1^{st} digit 4 from dividend 44
\begin{array}{l}\phantom{44)}0\phantom{2}\\44\overline{)44}\\\end{array}
Since 4 is less than 44, use the next digit 4 from dividend 44 and add 0 to the quotient
\begin{array}{l}\phantom{44)}0\phantom{3}\\44\overline{)44}\\\end{array}
Use the 2^{nd} digit 4 from dividend 44
\begin{array}{l}\phantom{44)}01\phantom{4}\\44\overline{)44}\\\phantom{44)}\underline{\phantom{}44\phantom{}}\\\phantom{44)99}0\\\end{array}
Find closest multiple of 44 to 44. We see that 1 \times 44 = 44 is the nearest. Now subtract 44 from 44 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }0
Since 0 is less than 44, stop the division. The reminder is 0. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.