6003 ÷ 6 = 1000 R3
We're going to perform division on 6003 with 6 as the divisor.

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

Step 2:
6 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 0 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 6

Step 3:
6 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 100
Subtract 0 from 0 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 4:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 1000
Subtract 0 from 3 to get 3.

The final result is 1000 with a remainder of 3.