We look at the division of 105665 by 86 
We're looking to find how many times 86 goes into 105665.

On to step 1:
The number 86 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 86

Going ahead to step 2:
If we divide 10 by 86, we get 0 and a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 86

Advancing to step 3:
86 can be fit into 105 1 times, resulting in a remainder of 19.
The next digit of our result is 1. 
Result so far: 1.0
If we take 86 away from 105, we end up with 19.
Bring next digit (6) of the dividend behind the 19 and repeat the process: 196 / 86

Let's proceed to step 4:
The number 86 fits into 196 2 times, leaving a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 12.0
Subtracting 172 from 196 leaves us with 24.
Fetch the next digit (6) from the dividend, attach it to 24 and continue: 246 / 86

Step 5:
The number 86 fits into 246 2 times, leaving a remainder of 74.
The number 2 becomes the next digit in our result. 
Result so far: 122.0
If we take 172 away from 246, we end up with 74.
Fetch the next digit (5) from the dividend, attach it to 74 and continue: 745 / 86

Moving on to step 6:
86 can be fit into 745 8 times, resulting in a remainder of 57.
Put 8 as the next digit of the answer. 
Result so far: 1228.0
Deduct 688 from 745 and we're left with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Moving on to step 7:
The number 86 fits into 570 6 times, leaving a remainder of 54.
Record the quotient 6 as the next digit in the result. 
Result so far: 1228.6
If we take 516 away from 570, we end up with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Advancing to step 8:
86 goes into 540 6 times with a remainder of 24.
Record the quotient 6 as the next digit in the result. 
Result so far: 1228.66
Subtracting 516 from 540 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The quotient of the division is 1228.66, and the remainder is 0.024.