66003 ÷ 6 = 11000 R3
Let's divide 66003 by 6.

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 (6) of the dividend behind the 0 and repeat the process: 6 / 6

Step 2:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 6 from 6 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: 110
Subtract 0 from 0 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 6

Step 4:
6 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 1100
Subtract 0 from 0 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 5:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 11000
Subtract 0 from 3 to get 3.

The final result is 11000 with a remainder of 3.