87643 ÷ 14 
Our goal is to divide 87643 by 14.

Let's proceed to step 1:
14 can be fit into 8 0 times, resulting in a remainder of 8.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Grab the next digit (7) from the dividend, add it to 8, then carry on: 87 / 14

Step 2:
The number 14 fits into 87 6 times, leaving a remainder of 3.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we take 84 away from 87, we end up with 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 14

Moving on to step 3:
The number 14 fits into 36 2 times, leaving a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 62.0
Subtract 28 from 36 to get 8.
Fetch the next digit (4) from the dividend, attach it to 8 and continue: 84 / 14

On to step 4:
84 divided by 14 is 6 with a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 626.0
The remainder is 0 after subtracting 84 from 84.
Fetch the next digit (3) from the dividend, attach it to 0 and continue: 3 / 14

Moving on to step 5:
If we divide 3 by 14, we get 0 and a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 6260.0
Subtract 0 from 3 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 6:
14 can be fit into 30 2 times, resulting in a remainder of 2.
The next digit of our result is 2. 
Result so far: 6260.2
If we subtract 28 from 30, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 7:
If we divide 20 by 14, we get 1 and a remainder of 6.
Write down 1 as next digit of the result. 
Result so far: 6260.21
Subtracting 14 from 20 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 8:
The number 14 fits into 60 4 times, leaving a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 6260.214
Subtract 56 from 60 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 9:
40 divided by 14 is 2 with a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 6260.2142
If we subtract 28 from 40, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 10:
120 divided by 14 is 8 with a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 6260.21428
Deduct 112 from 120 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 11:
When dividing 80 by 14, we get 5 with a remainder of 10.
The next digit of our result is 5. 
Result so far: 6260.214285
Subtracting 70 from 80 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.

Moving on to step 12:
If we divide 100 by 14, we get 7 and a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 6260.2142857
Deduct 98 from 100 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 13:
When dividing 20 by 14, we get 1 with a remainder of 6.
The next digit of our result is 1. 
Result so far: 6260.21428571
If we subtract 14 from 20, 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.

Our division results in 6260.21428571 with a remaining 6e-09.