8001 ÷ 3 = 2667 R0
Let's divide 8001 by 3.

Step 1:
3 goes into 8 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 6 from 8 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 3

Step 2:
3 goes into 20 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 26
Subtract 18 from 20 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 3

Step 3:
3 goes into 20 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 266
Subtract 18 from 20 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 3

Step 4:
3 goes into 21 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 2667
Subtract 21 from 21 to get 0.

The final result is 2667 with a remainder of 0.