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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)6876}\\\end{array}
Use the 1^{st} digit 6 from dividend 6876
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)6876}\\\end{array}
Since 6 is less than 54, use the next digit 8 from dividend 6876 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)6876}\\\end{array}
Use the 2^{nd} digit 8 from dividend 6876
\begin{array}{l}\phantom{54)}01\phantom{4}\\54\overline{)6876}\\\phantom{54)}\underline{\phantom{}54\phantom{99}}\\\phantom{54)}14\\\end{array}
Find closest multiple of 54 to 68. We see that 1 \times 54 = 54 is the nearest. Now subtract 54 from 68 to get reminder 14. Add 1 to quotient.
\begin{array}{l}\phantom{54)}01\phantom{5}\\54\overline{)6876}\\\phantom{54)}\underline{\phantom{}54\phantom{99}}\\\phantom{54)}147\\\end{array}
Use the 3^{rd} digit 7 from dividend 6876
\begin{array}{l}\phantom{54)}012\phantom{6}\\54\overline{)6876}\\\phantom{54)}\underline{\phantom{}54\phantom{99}}\\\phantom{54)}147\\\phantom{54)}\underline{\phantom{}108\phantom{9}}\\\phantom{54)9}39\\\end{array}
Find closest multiple of 54 to 147. We see that 2 \times 54 = 108 is the nearest. Now subtract 108 from 147 to get reminder 39. Add 2 to quotient.
\begin{array}{l}\phantom{54)}012\phantom{7}\\54\overline{)6876}\\\phantom{54)}\underline{\phantom{}54\phantom{99}}\\\phantom{54)}147\\\phantom{54)}\underline{\phantom{}108\phantom{9}}\\\phantom{54)9}396\\\end{array}
Use the 4^{th} digit 6 from dividend 6876
\begin{array}{l}\phantom{54)}0127\phantom{8}\\54\overline{)6876}\\\phantom{54)}\underline{\phantom{}54\phantom{99}}\\\phantom{54)}147\\\phantom{54)}\underline{\phantom{}108\phantom{9}}\\\phantom{54)9}396\\\phantom{54)}\underline{\phantom{9}378\phantom{}}\\\phantom{54)99}18\\\end{array}
Find closest multiple of 54 to 396. We see that 7 \times 54 = 378 is the nearest. Now subtract 378 from 396 to get reminder 18. Add 7 to quotient.
\text{Quotient: }127 \text{Reminder: }18
Since 18 is less than 54, stop the division. The reminder is 18. The topmost line 0127 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 127.