We're dividing 634689 by 42 
Our goal is to divide 634689 by 42.

Advancing to step 1:
6 divided by 42 is 0 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.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 42

Let's proceed to step 2:
63 divided by 42 is 1 with a remainder of 21.
The next digit of our result is 1. 
Result so far: 1.0
If we take 42 away from 63, we end up with 21.
Include the next digit (4) from the dividend after 21, then repeat: 214 / 42

Moving on to step 3:
If we divide 214 by 42, we get 5 and a remainder of 4.
Record the quotient 5 as the next digit in the result. 
Result so far: 15.0
If we subtract 210 from 214, we get 4.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 42

Moving on to step 4:
If we divide 46 by 42, we get 1 and a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 151.0
Deduct 42 from 46 and we're left with 4.
Fetch the next digit (8) from the dividend, attach it to 4 and continue: 48 / 42

Moving on to step 5:
The number 42 fits into 48 1 times, leaving a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 1511.0
If we take 42 away from 48, we end up with 6.
Take the next digit (9) from the dividend and append it to 6, then repeat: 69 / 42

On to step 6:
If we divide 69 by 42, we get 1 and a remainder of 27.
Put 1 as the next digit of the answer. 
Result so far: 15111.0
Subtract 42 from 69 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 7:
If we divide 270 by 42, we get 6 and a remainder of 18.
Record the quotient 6 as the next digit in the result. 
Result so far: 15111.6
Subtract 252 from 270 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 8:
When dividing 180 by 42, we get 4 with a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 15111.64
The remainder is 12 after subtracting 168 from 180.
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 9:
42 goes into 120 2 times with a remainder of 36.
Put 2 as the next digit of the answer. 
Result so far: 15111.642
Deduct 84 from 120 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 10:
42 goes into 360 8 times with a remainder of 24.
Record the quotient 8 as the next digit in the result. 
Result so far: 15111.6428
Deduct 336 from 360 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 11:
If we divide 240 by 42, we get 5 and a remainder of 30.
Put 5 as the next digit of the answer. 
Result so far: 15111.64285
The remainder is 30 after subtracting 210 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 12:
42 goes into 300 7 times with a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 15111.642857
The remainder is 6 after subtracting 294 from 300.
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 13:
If we divide 60 by 42, we get 1 and a remainder of 18.
Write down 1 as next digit of the result. 
Result so far: 15111.6428571
Subtract 42 from 60 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 14:
If we divide 180 by 42, we get 4 and a remainder of 12.
The next digit of our result is 4. 
Result so far: 15111.64285714
If we take 168 away from 180, 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.

In conclusion, the division gives 15111.64285714 with a balance of 1.2e-08.