We're dividing 75637 by 634 
We want to divide 75637 by 634.

Step 1:
The number 634 fits into 7 0 times, leaving a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Include the next digit (5) from the dividend after 7, then repeat: 75 / 634

Let's proceed to step 2:
When dividing 75 by 634, we get 0 with a remainder of 75.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 75 to get 75.
Append the next digit (6) from the dividend to 75 and continue with: 756 / 634

Step 3:
If we divide 756 by 634, we get 1 and a remainder of 122.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 634 from 756 to get 122.
Fetch the next digit (3) from the dividend, attach it to 122 and continue: 1223 / 634

Moving on to step 4:
The number 634 fits into 1223 1 times, leaving a remainder of 589.
Record the quotient 1 as the next digit in the result. 
Result so far: 11.0
If we take 634 away from 1223, we end up with 589.
Bring next digit (7) of the dividend behind the 589 and repeat the process: 5897 / 634

Step 5:
When dividing 5897 by 634, we get 9 with a remainder of 191.
Record the quotient 9 as the next digit in the result. 
Result so far: 119.0
Subtract 5706 from 5897 to get 191.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1910, and continue the process.

Advancing to step 6:
When dividing 1910 by 634, we get 3 with a remainder of 8.
Write down 3 as next digit of the result. 
Result so far: 119.3
Deduct 1902 from 1910 and we're left 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.

On to step 7:
If we divide 80 by 634, we get 0 and a remainder of 80.
Write down 0 as next digit of the result. 
Result so far: 119.3
Subtract 0 from 80 to get 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Moving on to step 8:
If we divide 800 by 634, we get 1 and a remainder of 166.
The number 1 becomes the next digit in our result. 
Result so far: 119.301
Deduct 634 from 800 and we're left with 166.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1660, and continue the process.

Moving on to step 9:
When dividing 1660 by 634, we get 2 with a remainder of 392.
Put 2 as the next digit of the answer. 
Result so far: 119.3012
If we subtract 1268 from 1660, we get 392.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3920, and continue the process.

Advancing to step 10:
634 goes into 3920 6 times with a remainder of 116.
Use 6 as the next digit of our solution. 
Result so far: 119.30126
Subtracting 3804 from 3920 leaves us with 116.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1160, and continue the process.

On to step 11:
634 can be fit into 1160 1 times, resulting in a remainder of 526.
Write down 1 as next digit of the result. 
Result so far: 119.301261
If we take 634 away from 1160, we end up with 526.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5260, and continue the process.

Advancing to step 12:
5260 divided by 634 is 8 with a remainder of 188.
The next digit of our result is 8. 
Result so far: 119.3012618
If we subtract 5072 from 5260, we get 188.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1880, and continue the process.

On to step 13:
If we divide 1880 by 634, we get 2 and a remainder of 612.
Put 2 as the next digit of the answer. 
Result so far: 119.30126182
Subtracting 1268 from 1880 leaves us with 612.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6120, and continue the process.

After the division, we end up with 119.30126182 and a remainder of 6.12e-07.