We're dividing 637607 by 14 
Our goal is to divide 637607 by 14.

Step 1:
14 goes into 6 0 times with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 14

Moving on to step 2:
When dividing 63 by 14, we get 4 with a remainder of 7.
The next digit of our result is 4. 
Result so far: 4.0
If we take 56 away from 63, we end up with 7.
Append the next digit (7) from the dividend to 7 and continue with: 77 / 14

Going ahead to step 3:
If we divide 77 by 14, we get 5 and a remainder of 7.
Write down 5 as next digit of the result. 
Result so far: 45.0
Subtracting 70 from 77 leaves us with 7.
Append the next digit (6) from the dividend to 7 and continue with: 76 / 14

Advancing to step 4:
14 can be fit into 76 5 times, resulting in a remainder of 6.
The next digit of our result is 5. 
Result so far: 455.0
The remainder is 6 after subtracting 70 from 76.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 14

On to step 5:
60 divided by 14 is 4 with a remainder of 4.
The next digit of our result is 4. 
Result so far: 4554.0
The remainder is 4 after subtracting 56 from 60.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 14

Moving on to step 6:
47 divided by 14 is 3 with a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 45543.0
If we subtract 42 from 47, we 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.

Advancing to step 7:
The number 14 fits into 50 3 times, leaving a remainder of 8.
Use 3 as the next digit of our solution. 
Result so far: 45543.3
Deduct 42 from 50 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.

Step 8:
80 divided by 14 is 5 with a remainder of 10.
The next digit of our result is 5. 
Result so far: 45543.35
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.

Step 9:
100 divided by 14 is 7 with a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 45543.357
Subtract 98 from 100 to 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.

Moving on to step 10:
The number 14 fits into 20 1 times, leaving a remainder of 6.
Record the quotient 1 as the next digit in the result. 
Result so far: 45543.3571
If we take 14 away from 20, we end up 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.

Going ahead to step 11:
14 goes into 60 4 times with a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 45543.35714
If we take 56 away from 60, we end up 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.

Moving on to step 12:
14 can be fit into 40 2 times, resulting in a remainder of 12.
Record the quotient 2 as the next digit in the result. 
Result so far: 45543.357142
If we take 28 away from 40, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 13:
14 can be fit into 120 8 times, resulting in a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 45543.3571428
The remainder is 8 after subtracting 112 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 14:
The number 14 fits into 80 5 times, leaving a remainder of 10.
The next digit of our result is 5. 
Result so far: 45543.35714285
The remainder is 10 after subtracting 70 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

In conclusion, the division gives 45543.35714285 with a balance of 1e-08.