15503 ÷ 3 = 5167 R2
Alright, let's work through the division of 15503 by 3 step by step.

Step 1:
3 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 (5) of the dividend behind the 1 and repeat the process: 15 / 3

Step 2:
3 goes into 15 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 15 from 15 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 3

Step 3:
3 goes into 5 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 51
Subtract 3 from 5 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 3

Step 4:
3 goes into 20 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 516
Subtract 18 from 20 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 3

Step 5:
3 goes into 23 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 5167
Subtract 21 from 23 to get 2.

The final result is 5167 with a remainder of 2.