We look at the division of 634307 by 42 
We want to figure out the number of times 634307 can be divided by 42.

Moving on to step 1:
When dividing 6 by 42, we get 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 42

On to step 2:
42 can be fit into 63 1 times, resulting in a remainder of 21.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 21 after subtracting 42 from 63.
Grab the next digit (4) from the dividend, add it to 21, then carry on: 214 / 42

Going ahead to step 3:
42 goes into 214 5 times with a remainder of 4.
Use 5 as the next digit of our solution. 
Result so far: 15.0
If we take 210 away from 214, we end up with 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 42

Step 4:
The number 42 fits into 43 1 times, leaving a remainder of 1.
The next digit of our result is 1. 
Result so far: 151.0
If we take 42 away from 43, we end up with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 42

Going ahead to step 5:
42 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 1510.0
If we take 0 away from 10, we end up with 10.
Fetch the next digit (7) from the dividend, attach it to 10 and continue: 107 / 42

Let's proceed to step 6:
42 goes into 107 2 times with a remainder of 23.
Use 2 as the next digit of our solution. 
Result so far: 15102.0
Subtracting 84 from 107 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 7:
The number 42 fits into 230 5 times, leaving a remainder of 20.
The number 5 becomes the next digit in our result. 
Result so far: 15102.5
If we subtract 210 from 230, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 8:
42 can be fit into 200 4 times, resulting in a remainder of 32.
Use 4 as the next digit of our solution. 
Result so far: 15102.54
If we take 168 away from 200, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 9:
320 divided by 42 is 7 with a remainder of 26.
Use 7 as the next digit of our solution. 
Result so far: 15102.547
If we subtract 294 from 320, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 10:
The number 42 fits into 260 6 times, leaving a remainder of 8.
Put 6 as the next digit of the answer. 
Result so far: 15102.5476
Subtracting 252 from 260 leaves us 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.

Advancing to step 11:
80 divided by 42 is 1 with a remainder of 38.
Put 1 as the next digit of the answer. 
Result so far: 15102.54761
Subtract 42 from 80 to get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 12:
When dividing 380 by 42, we get 9 with a remainder of 2.
The number 9 becomes the next digit in our result. 
Result so far: 15102.547619
If we take 378 away from 380, we end up 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.

Going ahead to step 13:
42 can be fit into 20 0 times, resulting in a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 15102.547619
If we take 0 away from 20, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 14:
200 divided by 42 is 4 with a remainder of 32.
Record the quotient 4 as the next digit in the result. 
Result so far: 15102.54761904
The remainder is 32 after subtracting 168 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The final result is 15102.54761904 with a remainder of 3.2e-08.