13603 ÷ 4 = 3400 R3
Alright, let's work through the division of 13603 by 4 step by step.

Step 1:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 4

Step 2:
4 goes into 13 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 12 from 13 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 4

Step 3:
4 goes into 16 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 34
Subtract 16 from 16 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 4

Step 4:
4 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 340
Subtract 0 from 0 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 4

Step 5:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 3400
Subtract 0 from 3 to get 3.

The final result is 3400 with a remainder of 3.