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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)3690}\\\end{array}
Use the 1^{st} digit 3 from dividend 3690
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)3690}\\\end{array}
Since 3 is less than 90, use the next digit 6 from dividend 3690 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)3690}\\\end{array}
Use the 2^{nd} digit 6 from dividend 3690
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)3690}\\\end{array}
Since 36 is less than 90, use the next digit 9 from dividend 3690 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)3690}\\\end{array}
Use the 3^{rd} digit 9 from dividend 3690
\begin{array}{l}\phantom{90)}004\phantom{6}\\90\overline{)3690}\\\phantom{90)}\underline{\phantom{}360\phantom{9}}\\\phantom{90)99}9\\\end{array}
Find closest multiple of 90 to 369. We see that 4 \times 90 = 360 is the nearest. Now subtract 360 from 369 to get reminder 9. Add 4 to quotient.
\begin{array}{l}\phantom{90)}004\phantom{7}\\90\overline{)3690}\\\phantom{90)}\underline{\phantom{}360\phantom{9}}\\\phantom{90)99}90\\\end{array}
Use the 4^{th} digit 0 from dividend 3690
\begin{array}{l}\phantom{90)}0041\phantom{8}\\90\overline{)3690}\\\phantom{90)}\underline{\phantom{}360\phantom{9}}\\\phantom{90)99}90\\\phantom{90)}\underline{\phantom{99}90\phantom{}}\\\phantom{90)9999}0\\\end{array}
Find closest multiple of 90 to 90. We see that 1 \times 90 = 90 is the nearest. Now subtract 90 from 90 to get reminder 0. Add 1 to quotient.
\text{Quotient: }41 \text{Reminder: }0
Since 0 is less than 90, stop the division. The reminder is 0. The topmost line 0041 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 41.