603134 ÷ 95 
Our goal is to divide 603134 by 95.

Going ahead to step 1:
The number 95 fits into 6 0 times, leaving a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Fetch the next digit (0) from the dividend, attach it to 6 and continue: 60 / 95

Advancing to step 2:
The number 95 fits into 60 0 times, leaving a remainder of 60.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 60, we end up with 60.
Append the next digit (3) from the dividend to 60 and continue with: 603 / 95

Step 3:
95 can be fit into 603 6 times, resulting in a remainder of 33.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtracting 570 from 603 leaves us with 33.
Take the next digit (1) from the dividend and append it to 33, then repeat: 331 / 95

Moving on to step 4:
95 goes into 331 3 times with a remainder of 46.
The next digit of our result is 3. 
Result so far: 63.0
If we take 285 away from 331, we end up with 46.
Fetch the next digit (3) from the dividend, attach it to 46 and continue: 463 / 95

Step 5:
When dividing 463 by 95, we get 4 with a remainder of 83.
Put 4 as the next digit of the answer. 
Result so far: 634.0
If we subtract 380 from 463, we get 83.
Include the next digit (4) from the dividend after 83, then repeat: 834 / 95

Step 6:
834 divided by 95 is 8 with a remainder of 74.
The next digit of our result is 8. 
Result so far: 6348.0
If we subtract 760 from 834, we get 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Step 7:
When dividing 740 by 95, we get 7 with a remainder of 75.
Record the quotient 7 as the next digit in the result. 
Result so far: 6348.7
If we take 665 away from 740, we end up with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Let's proceed to step 8:
95 can be fit into 750 7 times, resulting in a remainder of 85.
Use 7 as the next digit of our solution. 
Result so far: 6348.77
Subtract 665 from 750 to get 85.
Since there are no more digits in the dividend, we add a zero to the remainder making it 850, and continue the process.

After the division, we end up with 6348.77 and a remainder of 0.085.