Let's divide 109637 by 41
We're looking to find how many times 41 goes into 109637.

Step 1:
41 can be fit into 1 0 times, resulting in a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 41

Going ahead to step 2:
41 goes into 10 0 times with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 41

On to step 3:
109 divided by 41 is 2 with a remainder of 27.
Write down 2 as next digit of the result. 
Result so far: 2.0
Deduct 82 from 109 and we're left with 27.
Include the next digit (6) from the dividend after 27, then repeat: 276 / 41

Advancing to step 4:
276 divided by 41 is 6 with a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 26.0
If we take 246 away from 276, we end up with 30.
Include the next digit (3) from the dividend after 30, then repeat: 303 / 41

Let's proceed to step 5:
41 goes into 303 7 times with a remainder of 16.
Put 7 as the next digit of the answer. 
Result so far: 267.0
Subtract 287 from 303 to get 16.
Append the next digit (7) from the dividend to 16 and continue with: 167 / 41

Let's proceed to step 6:
When dividing 167 by 41, we get 4 with a remainder of 3.
The number 4 becomes the next digit in our result. 
Result so far: 2674.0
Subtracting 164 from 167 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 7:
When dividing 30 by 41, we get 0 with a remainder of 30.
The next digit of our result is 0. 
Result so far: 2674.0
Subtracting 0 from 30 leaves us 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.

Moving on to step 8:
300 divided by 41 is 7 with a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 2674.07
If we take 287 away from 300, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 9:
41 can be fit into 130 3 times, resulting in a remainder of 7.
The next digit of our result is 3. 
Result so far: 2674.073
If we subtract 123 from 130, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 10:
When dividing 70 by 41, we get 1 with a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 2674.0731
Subtracting 41 from 70 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Step 11:
When dividing 290 by 41, we get 7 with a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 2674.07317
Subtract 287 from 290 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 12:
If we divide 30 by 41, we get 0 and a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 2674.07317
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 13:
300 divided by 41 is 7 with a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 2674.0731707
If we subtract 287 from 300, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 14:
The number 41 fits into 130 3 times, leaving a remainder of 7.
The number 3 becomes the next digit in our result. 
Result so far: 2674.07317073
If we subtract 123 from 130, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

In conclusion, the division gives 2674.07317073 with a balance of 7e-09.