We're dividing 633684 by 37 
We're looking to find how many times 37 goes into 633684.

Advancing to step 1:
6 divided by 37 is 0 with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 37

Going ahead to step 2:
63 divided by 37 is 1 with a remainder of 26.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 37 from 63 and we're left with 26.
Include the next digit (3) from the dividend after 26, then repeat: 263 / 37

Going ahead to step 3:
37 goes into 263 7 times with a remainder of 4.
The next digit of our result is 7. 
Result so far: 17.0
If we take 259 away from 263, we end up with 4.
Append the next digit (6) from the dividend to 4 and continue with: 46 / 37

Moving on to step 4:
The number 37 fits into 46 1 times, leaving a remainder of 9.
The next digit of our result is 1. 
Result so far: 171.0
Subtracting 37 from 46 leaves us with 9.
Include the next digit (8) from the dividend after 9, then repeat: 98 / 37

On to step 5:
If we divide 98 by 37, we get 2 and a remainder of 24.
Record the quotient 2 as the next digit in the result. 
Result so far: 1712.0
If we take 74 away from 98, we end up with 24.
Grab the next digit (4) from the dividend, add it to 24, then carry on: 244 / 37

Going ahead to step 6:
37 can be fit into 244 6 times, resulting in a remainder of 22.
Use 6 as the next digit of our solution. 
Result so far: 17126.0
Subtracting 222 from 244 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.

Moving on to step 7:
37 can be fit into 220 5 times, resulting in a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 17126.5
Deduct 185 from 220 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 8:
If we divide 350 by 37, we get 9 and a remainder of 17.
Use 9 as the next digit of our solution. 
Result so far: 17126.59
Deduct 333 from 350 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

On to step 9:
37 goes into 170 4 times with a remainder of 22.
The next digit of our result is 4. 
Result so far: 17126.594
Subtract 148 from 170 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 10:
37 goes into 220 5 times with a remainder of 35.
The next digit of our result is 5. 
Result so far: 17126.5945
If we subtract 185 from 220, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 11:
37 goes into 350 9 times with a remainder of 17.
Record the quotient 9 as the next digit in the result. 
Result so far: 17126.59459
Subtract 333 from 350 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 12:
37 goes into 170 4 times with a remainder of 22.
The next digit of our result is 4. 
Result so far: 17126.594594
Deduct 148 from 170 and we're left 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.

On to step 13:
220 divided by 37 is 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 17126.5945945
The remainder is 35 after subtracting 185 from 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 14:
37 goes into 350 9 times with a remainder of 17.
Write down 9 as next digit of the result. 
Result so far: 17126.59459459
The remainder is 17 after subtracting 333 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

After the division, we end up with 17126.59459459 and a remainder of 1.7e-08.