6876 ÷ 4 = 1719 R0
Let's divide 6876 by 4.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 4

Step 2:
4 goes into 28 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 17
Subtract 28 from 28 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 4

Step 3:
4 goes into 7 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 171
Subtract 4 from 7 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 4

Step 4:
4 goes into 36 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 1719
Subtract 36 from 36 to get 0.

The final result is 1719 with a remainder of 0.