415634 ÷ 14 
Our goal is to divide 415634 by 14.

Advancing to step 1:
When dividing 4 by 14, we get 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 14

Moving on to step 2:
41 divided by 14 is 2 with a remainder of 13.
Put 2 as the next digit of the answer. 
Result so far: 2.0
If we take 28 away from 41, we end up with 13.
Take the next digit (5) from the dividend and append it to 13, then repeat: 135 / 14

Moving on to step 3:
When dividing 135 by 14, we get 9 with a remainder of 9.
Use 9 as the next digit of our solution. 
Result so far: 29.0
Deduct 126 from 135 and we're left with 9.
Include the next digit (6) from the dividend after 9, then repeat: 96 / 14

Moving on to step 4:
14 goes into 96 6 times with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 296.0
Subtracting 84 from 96 leaves us with 12.
Include the next digit (3) from the dividend after 12, then repeat: 123 / 14

Step 5:
14 can be fit into 123 8 times, resulting in a remainder of 11.
Use 8 as the next digit of our solution. 
Result so far: 2968.0
If we subtract 112 from 123, we get 11.
Grab the next digit (4) from the dividend, add it to 11, then carry on: 114 / 14

Going ahead to step 6:
14 goes into 114 8 times with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 29688.0
Subtracting 112 from 114 leaves us 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.

Step 7:
14 can be fit into 20 1 times, resulting in a remainder of 6.
The number 1 becomes the next digit in our result. 
Result so far: 29688.1
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.

Moving on to step 8:
60 divided by 14 is 4 with a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 29688.14
If we subtract 56 from 60, we 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.

Moving on to step 9:
40 divided by 14 is 2 with a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 29688.142
Subtracting 28 from 40 leaves us 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.

Let's proceed to step 10:
If we divide 120 by 14, we get 8 and a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 29688.1428
Subtract 112 from 120 to get 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:
80 divided by 14 is 5 with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 29688.14285
Deduct 70 from 80 and we're left 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 12:
If we divide 100 by 14, we get 7 and a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 29688.142857
If we subtract 98 from 100, 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.

On to step 13:
14 goes into 20 1 times with a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 29688.1428571
The remainder is 6 after subtracting 14 from 20.
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 14:
The number 14 fits into 60 4 times, leaving a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 29688.14285714
If we subtract 56 from 60, we 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.

The final result is 29688.14285714 with a remainder of 4e-09.