We look at the division of 706533 by 41 
We want to divide 706533 by 41.

On to step 1:
41 goes into 7 0 times with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Fetch the next digit (0) from the dividend, attach it to 7 and continue: 70 / 41

On to step 2:
The number 41 fits into 70 1 times, leaving a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 41 from 70, we get 29.
Include the next digit (6) from the dividend after 29, then repeat: 296 / 41

Step 3:
296 divided by 41 is 7 with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 17.0
The remainder is 9 after subtracting 287 from 296.
Bring next digit (5) of the dividend behind the 9 and repeat the process: 95 / 41

Step 4:
95 divided by 41 is 2 with a remainder of 13.
Put 2 as the next digit of the answer. 
Result so far: 172.0
Subtracting 82 from 95 leaves us with 13.
Take the next digit (3) from the dividend and append it to 13, then repeat: 133 / 41

Advancing to step 5:
When dividing 133 by 41, we get 3 with a remainder of 10.
The number 3 becomes the next digit in our result. 
Result so far: 1723.0
Deduct 123 from 133 and we're left with 10.
Bring next digit (3) of the dividend behind the 10 and repeat the process: 103 / 41

On to step 6:
If we divide 103 by 41, we get 2 and a remainder of 21.
The number 2 becomes the next digit in our result. 
Result so far: 17232.0
Subtract 82 from 103 to get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 7:
The number 41 fits into 210 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 17232.5
The remainder is 5 after subtracting 205 from 210.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 8:
50 divided by 41 is 1 with a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 17232.51
If we take 41 away from 50, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 9:
41 can be fit into 90 2 times, resulting in a remainder of 8.
The next digit of our result is 2. 
Result so far: 17232.512
If we subtract 82 from 90, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 10:
When dividing 80 by 41, we get 1 with a remainder of 39.
Record the quotient 1 as the next digit in the result. 
Result so far: 17232.5121
Deduct 41 from 80 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Going ahead to step 11:
If we divide 390 by 41, we get 9 and a remainder of 21.
Put 9 as the next digit of the answer. 
Result so far: 17232.51219
The remainder is 21 after subtracting 369 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 12:
210 divided by 41 is 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 17232.512195
If we take 205 away from 210, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 13:
When dividing 50 by 41, we get 1 with a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 17232.5121951
If we subtract 41 from 50, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 14:
When dividing 90 by 41, we get 2 with a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 17232.51219512
If we take 82 away from 90, we end up 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.

The final result is 17232.51219512 with a remainder of 8e-09.