25965196 divided by 821 
We want to divide 25965196 by 821.

Going ahead to step 1:
The number 821 fits into 2 0 times, leaving a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 821

On to step 2:
25 divided by 821 is 0 with a remainder of 25.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 25 to get 25.
Include the next digit (9) from the dividend after 25, then repeat: 259 / 821

Step 3:
If we divide 259 by 821, we get 0 and a remainder of 259.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 259 to get 259.
Include the next digit (6) from the dividend after 259, then repeat: 2596 / 821

Advancing to step 4:
When dividing 2596 by 821, we get 3 with a remainder of 133.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we subtract 2463 from 2596, we get 133.
Include the next digit (5) from the dividend after 133, then repeat: 1335 / 821

On to step 5:
The number 821 fits into 1335 1 times, leaving a remainder of 514.
Put 1 as the next digit of the answer. 
Result so far: 31.0
Deduct 821 from 1335 and we're left with 514.
Bring next digit (1) of the dividend behind the 514 and repeat the process: 5141 / 821

Advancing to step 6:
821 can be fit into 5141 6 times, resulting in a remainder of 215.
Record the quotient 6 as the next digit in the result. 
Result so far: 316.0
Deduct 4926 from 5141 and we're left with 215.
Take the next digit (9) from the dividend and append it to 215, then repeat: 2159 / 821

On to step 7:
When dividing 2159 by 821, we get 2 with a remainder of 517.
Write down 2 as next digit of the result. 
Result so far: 3162.0
The remainder is 517 after subtracting 1642 from 2159.
Include the next digit (6) from the dividend after 517, then repeat: 5176 / 821

Moving on to step 8:
5176 divided by 821 is 6 with a remainder of 250.
Write down 6 as next digit of the result. 
Result so far: 31626.0
The remainder is 250 after subtracting 4926 from 5176.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2500, and continue the process.

Going ahead to step 9:
If we divide 2500 by 821, we get 3 and a remainder of 37.
The number 3 becomes the next digit in our result. 
Result so far: 31626.3
If we subtract 2463 from 2500, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Moving on to step 10:
If we divide 370 by 821, we get 0 and a remainder of 370.
Write down 0 as next digit of the result. 
Result so far: 31626.3
Subtracting 0 from 370 leaves us with 370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3700, and continue the process.

Step 11:
3700 divided by 821 is 4 with a remainder of 416.
Use 4 as the next digit of our solution. 
Result so far: 31626.304
The remainder is 416 after subtracting 3284 from 3700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4160, and continue the process.

On to step 12:
821 goes into 4160 5 times with a remainder of 55.
The next digit of our result is 5. 
Result so far: 31626.3045
Deduct 4105 from 4160 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 13:
821 can be fit into 550 0 times, resulting in a remainder of 550.
Use 0 as the next digit of our solution. 
Result so far: 31626.3045
The remainder is 550 after subtracting 0 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5500, and continue the process.

Step 14:
821 goes into 5500 6 times with a remainder of 574.
Record the quotient 6 as the next digit in the result. 
Result so far: 31626.304506
Subtract 4926 from 5500 to get 574.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5740, and continue the process.

Let's proceed to step 15:
The number 821 fits into 5740 6 times, leaving a remainder of 814.
Put 6 as the next digit of the answer. 
Result so far: 31626.3045066
The remainder is 814 after subtracting 4926 from 5740.
Since there are no more digits in the dividend, we add a zero to the remainder making it 8140, and continue the process.

After the division, we end up with 31626.3045066 and a remainder of 8.14e-06.