637123 ÷ 41 
Our goal is to divide 637123 by 41.

Let's proceed to step 1:
41 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 41

On to step 2:
The number 41 fits into 63 1 times, leaving a remainder of 22.
The next digit of our result is 1. 
Result so far: 1.0
If we take 41 away from 63, we end up with 22.
Fetch the next digit (7) from the dividend, attach it to 22 and continue: 227 / 41

Advancing to step 3:
If we divide 227 by 41, we get 5 and a remainder of 22.
The next digit of our result is 5. 
Result so far: 15.0
Subtracting 205 from 227 leaves us with 22.
Include the next digit (1) from the dividend after 22, then repeat: 221 / 41

Moving on to step 4:
The number 41 fits into 221 5 times, leaving a remainder of 16.
The next digit of our result is 5. 
Result so far: 155.0
Subtracting 205 from 221 leaves us with 16.
Bring next digit (2) of the dividend behind the 16 and repeat the process: 162 / 41

Let's proceed to step 5:
162 divided by 41 is 3 with a remainder of 39.
Record the quotient 3 as the next digit in the result. 
Result so far: 1553.0
If we subtract 123 from 162, we get 39.
Take the next digit (3) from the dividend and append it to 39, then repeat: 393 / 41

Advancing to step 6:
41 goes into 393 9 times with a remainder of 24.
The number 9 becomes the next digit in our result. 
Result so far: 15539.0
If we subtract 369 from 393, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 7:
41 goes into 240 5 times with a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 15539.5
Subtracting 205 from 240 leaves us 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.

Going ahead to step 8:
When dividing 350 by 41, we get 8 with a remainder of 22.
Record the quotient 8 as the next digit in the result. 
Result so far: 15539.58
The remainder is 22 after subtracting 328 from 350.
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 9:
If we divide 220 by 41, we get 5 and a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 15539.585
If we subtract 205 from 220, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 10:
The number 41 fits into 150 3 times, leaving a remainder of 27.
The number 3 becomes the next digit in our result. 
Result so far: 15539.5853
The remainder is 27 after subtracting 123 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 11:
When dividing 270 by 41, we get 6 with a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 15539.58536
Subtract 246 from 270 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 12:
41 goes into 240 5 times with a remainder of 35.
Write down 5 as next digit of the result. 
Result so far: 15539.585365
The remainder is 35 after subtracting 205 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 13:
The number 41 fits into 350 8 times, leaving a remainder of 22.
The next digit of our result is 8. 
Result so far: 15539.5853658
If we take 328 away from 350, 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.

Moving on to step 14:
When dividing 220 by 41, we get 5 with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 15539.58536585
Deduct 205 from 220 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

After the division, we end up with 15539.58536585 and a remainder of 1.5e-08.