21059311 ÷ 965 
Our goal is to divide 21059311 by 965.

Advancing to step 1:
965 goes into 2 0 times with a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 965

On to step 2:
21 divided by 965 is 0 with a remainder of 21.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 21, we get 21.
Include the next digit (0) from the dividend after 21, then repeat: 210 / 965

Going ahead to step 3:
The number 965 fits into 210 0 times, leaving a remainder of 210.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 210, we end up with 210.
Grab the next digit (5) from the dividend, add it to 210, then carry on: 2105 / 965

Moving on to step 4:
When dividing 2105 by 965, we get 2 with a remainder of 175.
The next digit of our result is 2. 
Result so far: 2.0
Subtracting 1930 from 2105 leaves us with 175.
Append the next digit (9) from the dividend to 175 and continue with: 1759 / 965

On to step 5:
If we divide 1759 by 965, we get 1 and a remainder of 794.
Use 1 as the next digit of our solution. 
Result so far: 21.0
Subtract 965 from 1759 to get 794.
Fetch the next digit (3) from the dividend, attach it to 794 and continue: 7943 / 965

Let's proceed to step 6:
965 goes into 7943 8 times with a remainder of 223.
The next digit of our result is 8. 
Result so far: 218.0
Subtract 7720 from 7943 to get 223.
Include the next digit (1) from the dividend after 223, then repeat: 2231 / 965

Going ahead to step 7:
When dividing 2231 by 965, we get 2 with a remainder of 301.
Put 2 as the next digit of the answer. 
Result so far: 2182.0
The remainder is 301 after subtracting 1930 from 2231.
Append the next digit (1) from the dividend to 301 and continue with: 3011 / 965

Advancing to step 8:
965 can be fit into 3011 3 times, resulting in a remainder of 116.
The number 3 becomes the next digit in our result. 
Result so far: 21823.0
The remainder is 116 after subtracting 2895 from 3011.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1160, and continue the process.

Moving on to step 9:
965 can be fit into 1160 1 times, resulting in a remainder of 195.
The number 1 becomes the next digit in our result. 
Result so far: 21823.1
Deduct 965 from 1160 and we're left with 195.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1950, and continue the process.

Going ahead to step 10:
If we divide 1950 by 965, we get 2 and a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 21823.12
If we subtract 1930 from 1950, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 11:
965 can be fit into 200 0 times, resulting in a remainder of 200.
Record the quotient 0 as the next digit in the result. 
Result so far: 21823.12
Deduct 0 from 200 and we're left with 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2000, and continue the process.

Going ahead to step 12:
965 can be fit into 2000 2 times, resulting in a remainder of 70.
Put 2 as the next digit of the answer. 
Result so far: 21823.1202
If we take 1930 away from 2000, we end up with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Let's proceed to step 13:
700 divided by 965 is 0 with a remainder of 700.
Record the quotient 0 as the next digit in the result. 
Result so far: 21823.1202
The remainder is 700 after subtracting 0 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 7000, and continue the process.

Going ahead to step 14:
The number 965 fits into 7000 7 times, leaving a remainder of 245.
Use 7 as the next digit of our solution. 
Result so far: 21823.120207
Deduct 6755 from 7000 and we're left with 245.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2450, and continue the process.

On to step 15:
2450 divided by 965 is 2 with a remainder of 520.
Put 2 as the next digit of the answer. 
Result so far: 21823.1202072
Subtract 1930 from 2450 to get 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5200, and continue the process.

Let's proceed to step 16:
965 goes into 5200 5 times with a remainder of 375.
Record the quotient 5 as the next digit in the result. 
Result so far: 21823.12020725
The remainder is 375 after subtracting 4825 from 5200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3750, and continue the process.

Our division results in 21823.12020725 with a remaining 3.75e-07.