We look at the division of 6255439 by 953 
Let's see how many times 953 fits into 6255439.

Step 1:
When dividing 6 by 953, we get 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Append the next digit (2) from the dividend to 6 and continue with: 62 / 953

Advancing to step 2:
953 can be fit into 62 0 times, resulting in a remainder of 62.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 62 and we're left with 62.
Fetch the next digit (5) from the dividend, attach it to 62 and continue: 625 / 953

On to step 3:
If we divide 625 by 953, we get 0 and a remainder of 625.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 625 to get 625.
Append the next digit (5) from the dividend to 625 and continue with: 6255 / 953

Moving on to step 4:
The number 953 fits into 6255 6 times, leaving a remainder of 537.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Deduct 5718 from 6255 and we're left with 537.
Append the next digit (4) from the dividend to 537 and continue with: 5374 / 953

Advancing to step 5:
953 can be fit into 5374 5 times, resulting in a remainder of 609.
The number 5 becomes the next digit in our result. 
Result so far: 65.0
If we subtract 4765 from 5374, we get 609.
Grab the next digit (3) from the dividend, add it to 609, then carry on: 6093 / 953

Going ahead to step 6:
When dividing 6093 by 953, we get 6 with a remainder of 375.
The next digit of our result is 6. 
Result so far: 656.0
Subtract 5718 from 6093 to get 375.
Take the next digit (9) from the dividend and append it to 375, then repeat: 3759 / 953

Moving on to step 7:
3759 divided by 953 is 3 with a remainder of 900.
The number 3 becomes the next digit in our result. 
Result so far: 6563.0
If we subtract 2859 from 3759, we get 900.
Since there are no more digits in the dividend, we add a zero to the remainder making it 9000, and continue the process.

Step 8:
If we divide 9000 by 953, we get 9 and a remainder of 423.
Use 9 as the next digit of our solution. 
Result so far: 6563.9
Subtracting 8577 from 9000 leaves us with 423.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4230, and continue the process.

Step 9:
953 goes into 4230 4 times with a remainder of 418.
Write down 4 as next digit of the result. 
Result so far: 6563.94
If we take 3812 away from 4230, we end up with 418.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4180, and continue the process.

Moving on to step 10:
953 can be fit into 4180 4 times, resulting in a remainder of 368.
The next digit of our result is 4. 
Result so far: 6563.944
Deduct 3812 from 4180 and we're left with 368.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3680, and continue the process.

Our division results in 6563.944 with a remaining 0.0368.