61003 ÷ 6 = 10167 R1
No problem, we've got 61003 and 6 for the division.

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 (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 2:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 3:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 101
Subtract 6 from 10 to get 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 6

Step 4:
6 goes into 40 6 times with a remainder of 4.
Write down 6 as next digit of of the result. 
Result so far: 1016
Subtract 36 from 40 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

Step 5:
6 goes into 43 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 10167
Subtract 42 from 43 to get 1.

The final result is 10167 with a remainder of 1.