105197 divided by 85 
Our goal is to divide 105197 by 85.

On to step 1:
The number 85 fits into 1 0 times, leaving a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 85

Going ahead to step 2:
The number 85 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Grab the next digit (5) from the dividend, add it to 10, then carry on: 105 / 85

Advancing to step 3:
The number 85 fits into 105 1 times, leaving a remainder of 20.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 85 from 105 leaves us with 20.
Bring next digit (1) of the dividend behind the 20 and repeat the process: 201 / 85

Going ahead to step 4:
201 divided by 85 is 2 with a remainder of 31.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
Deduct 170 from 201 and we're left with 31.
Bring next digit (9) of the dividend behind the 31 and repeat the process: 319 / 85

Advancing to step 5:
85 goes into 319 3 times with a remainder of 64.
The number 3 becomes the next digit in our result. 
Result so far: 123.0
Deduct 255 from 319 and we're left with 64.
Include the next digit (7) from the dividend after 64, then repeat: 647 / 85

Advancing to step 6:
85 goes into 647 7 times with a remainder of 52.
The next digit of our result is 7. 
Result so far: 1237.0
The remainder is 52 after subtracting 595 from 647.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Step 7:
If we divide 520 by 85, we get 6 and a remainder of 10.
The next digit of our result is 6. 
Result so far: 1237.6
Subtracting 510 from 520 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 8:
85 can be fit into 100 1 times, resulting in a remainder of 15.
Put 1 as the next digit of the answer. 
Result so far: 1237.61
Subtracting 85 from 100 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 9:
The number 85 fits into 150 1 times, leaving a remainder of 65.
Write down 1 as next digit of the result. 
Result so far: 1237.611
If we take 85 away from 150, we end up with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

The final result is 1237.611 with a remainder of 0.0065.