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\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)6038}\\\end{array}
Use the 1^{st} digit 6 from dividend 6038
\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)6038}\\\end{array}
Since 6 is less than 1000, use the next digit 0 from dividend 6038 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)6038}\\\end{array}
Use the 2^{nd} digit 0 from dividend 6038
\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)6038}\\\end{array}
Since 60 is less than 1000, use the next digit 3 from dividend 6038 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)6038}\\\end{array}
Use the 3^{rd} digit 3 from dividend 6038
\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)6038}\\\end{array}
Since 603 is less than 1000, use the next digit 8 from dividend 6038 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)6038}\\\end{array}
Use the 4^{th} digit 8 from dividend 6038
\begin{array}{l}\phantom{1000)}0006\phantom{8}\\1000\overline{)6038}\\\phantom{1000)}\underline{\phantom{}6000\phantom{}}\\\phantom{1000)99}38\\\end{array}
Find closest multiple of 1000 to 6038. We see that 6 \times 1000 = 6000 is the nearest. Now subtract 6000 from 6038 to get reminder 38. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }38
Since 38 is less than 1000, stop the division. The reminder is 38. The topmost line 0006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.