We look at the division of 637584 by 34 
We're looking to find how many times 34 goes into 637584.

Let's proceed to step 1:
34 can be fit into 6 0 times, resulting in 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.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 34

Advancing to step 2:
34 can be fit into 63 1 times, resulting in a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 34 from 63 and we're left with 29.
Include the next digit (7) from the dividend after 29, then repeat: 297 / 34

Advancing to step 3:
297 divided by 34 is 8 with a remainder of 25.
The number 8 becomes the next digit in our result. 
Result so far: 18.0
Subtract 272 from 297 to get 25.
Bring next digit (5) of the dividend behind the 25 and repeat the process: 255 / 34

Moving on to step 4:
The number 34 fits into 255 7 times, leaving a remainder of 17.
Use 7 as the next digit of our solution. 
Result so far: 187.0
Deduct 238 from 255 and we're left with 17.
Fetch the next digit (8) from the dividend, attach it to 17 and continue: 178 / 34

Moving on to step 5:
34 goes into 178 5 times with a remainder of 8.
The next digit of our result is 5. 
Result so far: 1875.0
If we subtract 170 from 178, we get 8.
Take the next digit (4) from the dividend and append it to 8, then repeat: 84 / 34

Moving on to step 6:
When dividing 84 by 34, we get 2 with a remainder of 16.
The next digit of our result is 2. 
Result so far: 18752.0
Subtract 68 from 84 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 7:
If we divide 160 by 34, we get 4 and a remainder of 24.
Record the quotient 4 as the next digit in the result. 
Result so far: 18752.4
If we take 136 away from 160, we end up 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.

Step 8:
If we divide 240 by 34, we get 7 and a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 18752.47
If we take 238 away from 240, 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.

Let's proceed to step 9:
34 goes into 20 0 times with a remainder of 20.
Use 0 as the next digit of our solution. 
Result so far: 18752.47
Subtracting 0 from 20 leaves us 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 10:
The number 34 fits into 200 5 times, leaving a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 18752.4705
Deduct 170 from 200 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 11:
If we divide 300 by 34, we get 8 and a remainder of 28.
Record the quotient 8 as the next digit in the result. 
Result so far: 18752.47058
Deduct 272 from 300 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 12:
When dividing 280 by 34, we get 8 with a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 18752.470588
Subtract 272 from 280 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.

After the division, we end up with 18752.470588 and a remainder of 8e-07.