We look at the division of 71414137 by 517 
Our goal is to divide 71414137 by 517.

On to step 1:
The number 517 fits into 7 0 times, leaving a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Take the next digit (1) from the dividend and append it to 7, then repeat: 71 / 517

Step 2:
517 can be fit into 71 0 times, resulting in a remainder of 71.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 71, we end up with 71.
Include the next digit (4) from the dividend after 71, then repeat: 714 / 517

Let's proceed to step 3:
The number 517 fits into 714 1 times, leaving a remainder of 197.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 517 away from 714, we end up with 197.
Fetch the next digit (1) from the dividend, attach it to 197 and continue: 1971 / 517

Going ahead to step 4:
517 goes into 1971 3 times with a remainder of 420.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
Subtracting 1551 from 1971 leaves us with 420.
Include the next digit (4) from the dividend after 420, then repeat: 4204 / 517

Step 5:
The number 517 fits into 4204 8 times, leaving a remainder of 68.
Use 8 as the next digit of our solution. 
Result so far: 138.0
Subtract 4136 from 4204 to get 68.
Fetch the next digit (1) from the dividend, attach it to 68 and continue: 681 / 517

On to step 6:
517 can be fit into 681 1 times, resulting in a remainder of 164.
The number 1 becomes the next digit in our result. 
Result so far: 1381.0
Subtract 517 from 681 to get 164.
Fetch the next digit (3) from the dividend, attach it to 164 and continue: 1643 / 517

Going ahead to step 7:
The number 517 fits into 1643 3 times, leaving a remainder of 92.
The next digit of our result is 3. 
Result so far: 13813.0
If we take 1551 away from 1643, we end up with 92.
Grab the next digit (7) from the dividend, add it to 92, then carry on: 927 / 517

Let's proceed to step 8:
517 can be fit into 927 1 times, resulting in a remainder of 410.
Put 1 as the next digit of the answer. 
Result so far: 138131.0
If we subtract 517 from 927, we get 410.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4100, and continue the process.

Going ahead to step 9:
When dividing 4100 by 517, we get 7 with a remainder of 481.
Use 7 as the next digit of our solution. 
Result so far: 138131.7
Deduct 3619 from 4100 and we're left with 481.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4810, and continue the process.

Moving on to step 10:
517 can be fit into 4810 9 times, resulting in a remainder of 157.
Write down 9 as next digit of the result. 
Result so far: 138131.79
The remainder is 157 after subtracting 4653 from 4810.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1570, and continue the process.

On to step 11:
517 can be fit into 1570 3 times, resulting in a remainder of 19.
Use 3 as the next digit of our solution. 
Result so far: 138131.793
The remainder is 19 after subtracting 1551 from 1570.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Going ahead to step 12:
The number 517 fits into 190 0 times, leaving a remainder of 190.
Record the quotient 0 as the next digit in the result. 
Result so far: 138131.793
Subtract 0 from 190 to get 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1900, and continue the process.

Let's proceed to step 13:
If we divide 1900 by 517, we get 3 and a remainder of 349.
The next digit of our result is 3. 
Result so far: 138131.79303
The remainder is 349 after subtracting 1551 from 1900.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3490, and continue the process.

Going ahead to step 14:
The number 517 fits into 3490 6 times, leaving a remainder of 388.
Record the quotient 6 as the next digit in the result. 
Result so far: 138131.793036
The remainder is 388 after subtracting 3102 from 3490.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3880, and continue the process.

Moving on to step 15:
When dividing 3880 by 517, we get 7 with a remainder of 261.
The number 7 becomes the next digit in our result. 
Result so far: 138131.7930367
If we take 3619 away from 3880, we end up with 261.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2610, and continue the process.

Going ahead to step 16:
If we divide 2610 by 517, we get 5 and a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 138131.79303675
Subtracting 2585 from 2610 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

After the division, we end up with 138131.79303675 and a remainder of 2.5e-08.