We look at the division of 637241 by 43 
We want to figure out the number of times 637241 can be divided by 43.

Advancing to step 1:
6 divided by 43 is 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Append the next digit (3) from the dividend to 6 and continue with: 63 / 43

Let's proceed to step 2:
The number 43 fits into 63 1 times, leaving a remainder of 20.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 43 from 63, we get 20.
Include the next digit (7) from the dividend after 20, then repeat: 207 / 43

Step 3:
43 can be fit into 207 4 times, resulting in a remainder of 35.
Record the quotient 4 as the next digit in the result. 
Result so far: 14.0
Subtract 172 from 207 to get 35.
Bring next digit (2) of the dividend behind the 35 and repeat the process: 352 / 43

Going ahead to step 4:
If we divide 352 by 43, we get 8 and a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 148.0
If we take 344 away from 352, we end up with 8.
Fetch the next digit (4) from the dividend, attach it to 8 and continue: 84 / 43

Step 5:
When dividing 84 by 43, we get 1 with a remainder of 41.
The number 1 becomes the next digit in our result. 
Result so far: 1481.0
If we take 43 away from 84, we end up with 41.
Bring next digit (1) of the dividend behind the 41 and repeat the process: 411 / 43

Going ahead to step 6:
411 divided by 43 is 9 with a remainder of 24.
Record the quotient 9 as the next digit in the result. 
Result so far: 14819.0
The remainder is 24 after subtracting 387 from 411.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 7:
43 goes into 240 5 times with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 14819.5
The remainder is 25 after subtracting 215 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 8:
When dividing 250 by 43, we get 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 14819.55
Deduct 215 from 250 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.

The quotient of the division is 14819.55, and the remainder is 0.035.