We look at the division of 966533 by 71 
We're looking to find how many times 71 goes into 966533.

Step 1:
When dividing 9 by 71, we get 0 with a remainder of 9.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 9, we get 9.
Append the next digit (6) from the dividend to 9 and continue with: 96 / 71

Let's proceed to step 2:
96 divided by 71 is 1 with a remainder of 25.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 71 from 96 and we're left with 25.
Include the next digit (6) from the dividend after 25, then repeat: 256 / 71

Let's proceed to step 3:
If we divide 256 by 71, we get 3 and a remainder of 43.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
If we take 213 away from 256, we end up with 43.
Bring next digit (5) of the dividend behind the 43 and repeat the process: 435 / 71

Going ahead to step 4:
71 can be fit into 435 6 times, resulting in a remainder of 9.
Write down 6 as next digit of the result. 
Result so far: 136.0
The remainder is 9 after subtracting 426 from 435.
Include the next digit (3) from the dividend after 9, then repeat: 93 / 71

Let's proceed to step 5:
When dividing 93 by 71, we get 1 with a remainder of 22.
Use 1 as the next digit of our solution. 
Result so far: 1361.0
Deduct 71 from 93 and we're left with 22.
Include the next digit (3) from the dividend after 22, then repeat: 223 / 71

Going ahead to step 6:
71 can be fit into 223 3 times, resulting in a remainder of 10.
The next digit of our result is 3. 
Result so far: 13613.0
The remainder is 10 after subtracting 213 from 223.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 7:
71 goes into 100 1 times with a remainder of 29.
Use 1 as the next digit of our solution. 
Result so far: 13613.1
Deduct 71 from 100 and we're left 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.

On to step 8:
The number 71 fits into 290 4 times, leaving a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 13613.14
The remainder is 6 after subtracting 284 from 290.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 9:
71 goes into 60 0 times with a remainder of 60.
Use 0 as the next digit of our solution. 
Result so far: 13613.14
If we subtract 0 from 60, we get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 10:
If we divide 600 by 71, we get 8 and a remainder of 32.
Record the quotient 8 as the next digit in the result. 
Result so far: 13613.1408
The remainder is 32 after subtracting 568 from 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Advancing to step 11:
71 goes into 320 4 times with a remainder of 36.
The number 4 becomes the next digit in our result. 
Result so far: 13613.14084
If we subtract 284 from 320, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 12:
71 goes into 360 5 times with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 13613.140845
Subtracting 355 from 360 leaves us 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.

Step 13:
50 divided by 71 is 0 with a remainder of 50.
Put 0 as the next digit of the answer. 
Result so far: 13613.140845
If we subtract 0 from 50, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Step 14:
When dividing 500 by 71, we get 7 with a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 13613.14084507
If we subtract 497 from 500, we 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.

The final result is 13613.14084507 with a remainder of 3e-09.