503 ÷ 4 = 125 R3
Alright, let's work through the division of 503 by 4 step by step.

Step 1:
4 goes into 5 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 5 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 4

Step 2:
4 goes into 10 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 8 from 10 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 4

Step 3:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 125
Subtract 20 from 23 to get 3.

The final result is 125 with a remainder of 3.