10603 ÷ 86 
Our goal is to divide 10603 by 86.

Step 1:
86 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 86

Advancing to step 2:
If we divide 10 by 86, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 86

Advancing to step 3:
The number 86 fits into 106 1 times, leaving a remainder of 20.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 86 from 106, we get 20.
Grab the next digit (0) from the dividend, add it to 20, then carry on: 200 / 86

Let's proceed to step 4:
200 divided by 86 is 2 with a remainder of 28.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Deduct 172 from 200 and we're left with 28.
Append the next digit (3) from the dividend to 28 and continue with: 283 / 86

On to step 5:
The number 86 fits into 283 3 times, leaving a remainder of 25.
The number 3 becomes the next digit in our result. 
Result so far: 123.0
If we subtract 258 from 283, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 6:
If we divide 250 by 86, we get 2 and a remainder of 78.
The number 2 becomes the next digit in our result. 
Result so far: 123.2
If we take 172 away from 250, we end up with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Step 7:
86 can be fit into 780 9 times, resulting in a remainder of 6.
Use 9 as the next digit of our solution. 
Result so far: 123.29
If we subtract 774 from 780, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 8:
86 goes into 60 0 times with a remainder of 60.
Put 0 as the next digit of the answer. 
Result so far: 123.29
Deduct 0 from 60 and we're left with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 9:
86 goes into 600 6 times with a remainder of 84.
Put 6 as the next digit of the answer. 
Result so far: 123.2906
If we subtract 516 from 600, we get 84.
Since there are no more digits in the dividend, we add a zero to the remainder making it 840, and continue the process.

Step 10:
86 can be fit into 840 9 times, resulting in a remainder of 66.
Put 9 as the next digit of the answer. 
Result so far: 123.29069
Deduct 774 from 840 and we're left with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Going ahead to step 11:
86 goes into 660 7 times with a remainder of 58.
Use 7 as the next digit of our solution. 
Result so far: 123.290697
The remainder is 58 after subtracting 602 from 660.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Let's proceed to step 12:
86 can be fit into 580 6 times, resulting in a remainder of 64.
Use 6 as the next digit of our solution. 
Result so far: 123.2906976
Subtract 516 from 580 to get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Let's proceed to step 13:
If we divide 640 by 86, we get 7 and a remainder of 38.
The number 7 becomes the next digit in our result. 
Result so far: 123.29069767
If we subtract 602 from 640, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Our division results in 123.29069767 with a remaining 3.8e-08.