We look at the division of 43974 by 41 
We want to figure out the number of times 43974 can be divided by 41.

On to step 1:
4 divided by 41 is 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 41

On to step 2:
When dividing 43 by 41, we get 1 with a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 41 from 43 leaves us with 2.
Take the next digit (9) from the dividend and append it to 2, then repeat: 29 / 41

Moving on to step 3:
29 divided by 41 is 0 with a remainder of 29.
The next digit of our result is 0. 
Result so far: 10.0
If we take 0 away from 29, we end up with 29.
Include the next digit (7) from the dividend after 29, then repeat: 297 / 41

Going ahead to step 4:
When dividing 297 by 41, we get 7 with a remainder of 10.
The next digit of our result is 7. 
Result so far: 107.0
Deduct 287 from 297 and we're left with 10.
Take the next digit (4) from the dividend and append it to 10, then repeat: 104 / 41

Moving on to step 5:
41 goes into 104 2 times with a remainder of 22.
The number 2 becomes the next digit in our result. 
Result so far: 1072.0
Deduct 82 from 104 and we're left 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 6:
When dividing 220 by 41, we get 5 with a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 1072.5
Subtracting 205 from 220 leaves us 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.

On to step 7:
The number 41 fits into 150 3 times, leaving a remainder of 27.
Put 3 as the next digit of the answer. 
Result so far: 1072.53
Subtract 123 from 150 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

On to step 8:
If we divide 270 by 41, we get 6 and a remainder of 24.
The number 6 becomes the next digit in our result. 
Result so far: 1072.536
Deduct 246 from 270 and we're left 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.

Let's proceed to step 9:
The number 41 fits into 240 5 times, leaving a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 1072.5365
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.

Going ahead to step 10:
41 can be fit into 350 8 times, resulting in a remainder of 22.
Put 8 as the next digit of the answer. 
Result so far: 1072.53658
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.

Advancing to step 11:
41 can be fit into 220 5 times, resulting in a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 1072.536585
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.

On to step 12:
If we divide 150 by 41, we get 3 and a remainder of 27.
The number 3 becomes the next digit in our result. 
Result so far: 1072.5365853
Subtracting 123 from 150 leaves us with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 13:
When dividing 270 by 41, we get 6 with a remainder of 24.
Record the quotient 6 as the next digit in the result. 
Result so far: 1072.53658536
If we take 246 away from 270, 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.

The quotient of the division is 1072.53658536, and the remainder is 2.4e-08.