Let's divide 553138 by 3
We want to figure out the number of times 553138 can be divided by 3.

Going ahead to step 1:
The number 3 fits into 5 1 times, leaving a remainder of 2.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 3 from 5 to get 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 3

Moving on to step 2:
The number 3 fits into 25 8 times, leaving a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 18.0
Subtract 24 from 25 to get 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 3

Advancing to step 3:
3 can be fit into 13 4 times, resulting in a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 184.0
If we subtract 12 from 13, we get 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 3

Step 4:
11 divided by 3 is 3 with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 1843.0
Deduct 9 from 11 and we're left with 2.
Include the next digit (3) from the dividend after 2, then repeat: 23 / 3

On to step 5:
The number 3 fits into 23 7 times, leaving a remainder of 2.
The next digit of our result is 7. 
Result so far: 18437.0
Subtract 21 from 23 to get 2.
Fetch the next digit (8) from the dividend, attach it to 2 and continue: 28 / 3

Going ahead to step 6:
The number 3 fits into 28 9 times, leaving a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 184379.0
Deduct 27 from 28 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
3 goes into 10 3 times with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 184379.3
The remainder is 1 after subtracting 9 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 8:
10 divided by 3 is 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 184379.33
If we subtract 9 from 10, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

After the division, we end up with 184379.33 and a remainder of 0.001.