We're dividing 637663 by 42 
Our goal is to divide 637663 by 42.

Going ahead to step 1:
42 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 42

On to step 2:
63 divided by 42 is 1 with a remainder of 21.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 21 after subtracting 42 from 63.
Include the next digit (7) from the dividend after 21, then repeat: 217 / 42

Going ahead to step 3:
42 can be fit into 217 5 times, resulting in a remainder of 7.
The next digit of our result is 5. 
Result so far: 15.0
The remainder is 7 after subtracting 210 from 217.
Grab the next digit (6) from the dividend, add it to 7, then carry on: 76 / 42

Moving on to step 4:
When dividing 76 by 42, we get 1 with a remainder of 34.
The number 1 becomes the next digit in our result. 
Result so far: 151.0
Subtracting 42 from 76 leaves us with 34.
Take the next digit (6) from the dividend and append it to 34, then repeat: 346 / 42

On to step 5:
42 goes into 346 8 times with a remainder of 10.
Put 8 as the next digit of the answer. 
Result so far: 1518.0
Subtracting 336 from 346 leaves us with 10.
Fetch the next digit (3) from the dividend, attach it to 10 and continue: 103 / 42

Step 6:
42 goes into 103 2 times with a remainder of 19.
Use 2 as the next digit of our solution. 
Result so far: 15182.0
Subtracting 84 from 103 leaves us with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Step 7:
42 can be fit into 190 4 times, resulting in a remainder of 22.
The number 4 becomes the next digit in our result. 
Result so far: 15182.4
Subtracting 168 from 190 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 8:
If we divide 220 by 42, we get 5 and a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 15182.45
Subtract 210 from 220 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 9:
If we divide 100 by 42, we get 2 and a remainder of 16.
Use 2 as the next digit of our solution. 
Result so far: 15182.452
If we take 84 away from 100, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 10:
If we divide 160 by 42, we get 3 and a remainder of 34.
Use 3 as the next digit of our solution. 
Result so far: 15182.4523
The remainder is 34 after subtracting 126 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Let's proceed to step 11:
The number 42 fits into 340 8 times, leaving a remainder of 4.
The next digit of our result is 8. 
Result so far: 15182.45238
Subtracting 336 from 340 leaves us 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:
42 can be fit into 40 0 times, resulting in a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 15182.45238
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 13:
42 can be fit into 400 9 times, resulting in a remainder of 22.
Use 9 as the next digit of our solution. 
Result so far: 15182.4523809
If we take 378 away from 400, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 14:
42 can be fit into 220 5 times, resulting in a remainder of 10.
The next digit of our result is 5. 
Result so far: 15182.45238095
If we take 210 away from 220, we end up 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.

The final outcome is 15182.45238095, with a leftover of 1e-08.