34429571 ÷ 966 
Our goal is to divide 34429571 by 966.

Advancing to step 1:
966 goes into 3 0 times with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 966

Step 2:
34 divided by 966 is 0 with a remainder of 34.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 34, we get 34.
Append the next digit (4) from the dividend to 34 and continue with: 344 / 966

On to step 3:
344 divided by 966 is 0 with a remainder of 344.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 344, we get 344.
Bring next digit (2) of the dividend behind the 344 and repeat the process: 3442 / 966

Moving on to step 4:
When dividing 3442 by 966, we get 3 with a remainder of 544.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Subtracting 2898 from 3442 leaves us with 544.
Include the next digit (9) from the dividend after 544, then repeat: 5449 / 966

Moving on to step 5:
The number 966 fits into 5449 5 times, leaving a remainder of 619.
Record the quotient 5 as the next digit in the result. 
Result so far: 35.0
Subtract 4830 from 5449 to get 619.
Grab the next digit (5) from the dividend, add it to 619, then carry on: 6195 / 966

Going ahead to step 6:
966 goes into 6195 6 times with a remainder of 399.
The number 6 becomes the next digit in our result. 
Result so far: 356.0
If we subtract 5796 from 6195, we get 399.
Append the next digit (7) from the dividend to 399 and continue with: 3997 / 966

Step 7:
When dividing 3997 by 966, we get 4 with a remainder of 133.
Put 4 as the next digit of the answer. 
Result so far: 3564.0
If we subtract 3864 from 3997, we get 133.
Bring next digit (1) of the dividend behind the 133 and repeat the process: 1331 / 966

Advancing to step 8:
1331 divided by 966 is 1 with a remainder of 365.
Record the quotient 1 as the next digit in the result. 
Result so far: 35641.0
If we take 966 away from 1331, we end up with 365.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3650, and continue the process.

Moving on to step 9:
If we divide 3650 by 966, we get 3 and a remainder of 752.
Use 3 as the next digit of our solution. 
Result so far: 35641.3
If we take 2898 away from 3650, we end up with 752.
Since there are no more digits in the dividend, we add a zero to the remainder making it 7520, and continue the process.

On to step 10:
If we divide 7520 by 966, we get 7 and a remainder of 758.
Put 7 as the next digit of the answer. 
Result so far: 35641.37
If we subtract 6762 from 7520, we get 758.
Since there are no more digits in the dividend, we add a zero to the remainder making it 7580, and continue the process.

Step 11:
If we divide 7580 by 966, we get 7 and a remainder of 818.
Put 7 as the next digit of the answer. 
Result so far: 35641.377
Deduct 6762 from 7580 and we're left with 818.
Since there are no more digits in the dividend, we add a zero to the remainder making it 8180, and continue the process.

The final result is 35641.377 with a remainder of 0.0818.