953813 divided by 75 
Our goal is to divide 953813 by 75.

Let's proceed to step 1:
If we divide 9 by 75, we get 0 and a remainder of 9.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Append the next digit (5) from the dividend to 9 and continue with: 95 / 75

Going ahead to step 2:
95 divided by 75 is 1 with a remainder of 20.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 75 from 95, we get 20.
Take the next digit (3) from the dividend and append it to 20, then repeat: 203 / 75

Going ahead to step 3:
203 divided by 75 is 2 with a remainder of 53.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
Subtracting 150 from 203 leaves us with 53.
Append the next digit (8) from the dividend to 53 and continue with: 538 / 75

On to step 4:
If we divide 538 by 75, we get 7 and a remainder of 13.
Use 7 as the next digit of our solution. 
Result so far: 127.0
Subtract 525 from 538 to get 13.
Fetch the next digit (1) from the dividend, attach it to 13 and continue: 131 / 75

Advancing to step 5:
75 goes into 131 1 times with a remainder of 56.
Record the quotient 1 as the next digit in the result. 
Result so far: 1271.0
Subtract 75 from 131 to get 56.
Bring next digit (3) of the dividend behind the 56 and repeat the process: 563 / 75

Step 6:
75 can be fit into 563 7 times, resulting in a remainder of 38.
Record the quotient 7 as the next digit in the result. 
Result so far: 12717.0
Deduct 525 from 563 and we're left with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Let's proceed to step 7:
75 can be fit into 380 5 times, resulting in a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 12717.5
Subtract 375 from 380 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
75 goes into 50 0 times with a remainder of 50.
The next digit of our result is 0. 
Result so far: 12717.5
Subtract 0 from 50 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 9:
When dividing 500 by 75, we get 6 with a remainder of 50.
Use 6 as the next digit of our solution. 
Result so far: 12717.506
If we subtract 450 from 500, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 10:
75 can be fit into 500 6 times, resulting in a remainder of 50.
The number 6 becomes the next digit in our result. 
Result so far: 12717.5066
If we subtract 450 from 500, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The final result is 12717.5066 with a remainder of 0.0005.