We're dividing 14641 by 17 
We want to figure out the number of times 14641 can be divided by 17.

On to step 1:
The number 17 fits into 1 0 times, leaving a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (4) from the dividend after 1, then repeat: 14 / 17

On to step 2:
If we divide 14 by 17, we get 0 and a remainder of 14.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 14 leaves us with 14.
Grab the next digit (6) from the dividend, add it to 14, then carry on: 146 / 17

Advancing to step 3:
The number 17 fits into 146 8 times, leaving a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Subtract 136 from 146 to get 10.
Fetch the next digit (4) from the dividend, attach it to 10 and continue: 104 / 17

Going ahead to step 4:
17 can be fit into 104 6 times, resulting in a remainder of 2.
The next digit of our result is 6. 
Result so far: 86.0
The remainder is 2 after subtracting 102 from 104.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 17

Going ahead to step 5:
17 can be fit into 21 1 times, resulting in a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 861.0
Subtracting 17 from 21 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 6:
When dividing 40 by 17, we get 2 with a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 861.2
The remainder is 6 after subtracting 34 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 7:
17 goes into 60 3 times with a remainder of 9.
Record the quotient 3 as the next digit in the result. 
Result so far: 861.23
Subtracting 51 from 60 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 8:
90 divided by 17 is 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 861.235
Subtract 85 from 90 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.

Step 9:
17 goes into 50 2 times with a remainder of 16.
The next digit of our result is 2. 
Result so far: 861.2352
If we take 34 away from 50, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 10:
The number 17 fits into 160 9 times, leaving a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 861.23529
Subtract 153 from 160 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 11:
The number 17 fits into 70 4 times, leaving a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 861.235294
Deduct 68 from 70 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.

Advancing to step 12:
17 goes into 20 1 times with a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 861.2352941
If we subtract 17 from 20, we 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.

Moving on to step 13:
30 divided by 17 is 1 with a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 861.23529411
Subtracting 17 from 30 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Our division results in 861.23529411 with a remaining 1.3e-08.