8553 ÷ 6 = 1425 R3
Alright, let's work through the division of 8553 by 6 step by step.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 6

Step 2:
6 goes into 25 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 24 from 25 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 6

Step 3:
6 goes into 15 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 142
Subtract 12 from 15 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 4:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 1425
Subtract 30 from 33 to get 3.

The final result is 1425 with a remainder of 3.