10641289 divided by 259 
Our goal is to divide 10641289 by 259.

On to step 1:
When dividing 1 by 259, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 259

Going ahead to step 2:
259 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Include the next digit (6) from the dividend after 10, then repeat: 106 / 259

Step 3:
The number 259 fits into 106 0 times, leaving a remainder of 106.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 106, we end up with 106.
Bring next digit (4) of the dividend behind the 106 and repeat the process: 1064 / 259

Step 4:
259 can be fit into 1064 4 times, resulting in a remainder of 28.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
Subtracting 1036 from 1064 leaves us with 28.
Append the next digit (1) from the dividend to 28 and continue with: 281 / 259

On to step 5:
259 goes into 281 1 times with a remainder of 22.
Use 1 as the next digit of our solution. 
Result so far: 41.0
The remainder is 22 after subtracting 259 from 281.
Fetch the next digit (2) from the dividend, attach it to 22 and continue: 222 / 259

On to step 6:
If we divide 222 by 259, we get 0 and a remainder of 222.
The next digit of our result is 0. 
Result so far: 410.0
If we subtract 0 from 222, we get 222.
Append the next digit (8) from the dividend to 222 and continue with: 2228 / 259

Going ahead to step 7:
When dividing 2228 by 259, we get 8 with a remainder of 156.
The next digit of our result is 8. 
Result so far: 4108.0
Subtract 2072 from 2228 to get 156.
Include the next digit (9) from the dividend after 156, then repeat: 1569 / 259

Moving on to step 8:
The number 259 fits into 1569 6 times, leaving a remainder of 15.
The number 6 becomes the next digit in our result. 
Result so far: 41086.0
Subtracting 1554 from 1569 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 9:
When dividing 150 by 259, we get 0 with a remainder of 150.
Record the quotient 0 as the next digit in the result. 
Result so far: 41086.0
Subtracting 0 from 150 leaves us with 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1500, and continue the process.

On to step 10:
The number 259 fits into 1500 5 times, leaving a remainder of 205.
Write down 5 as next digit of the result. 
Result so far: 41086.05
Deduct 1295 from 1500 and we're left with 205.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2050, and continue the process.

On to step 11:
2050 divided by 259 is 7 with a remainder of 237.
The next digit of our result is 7. 
Result so far: 41086.057
Subtract 1813 from 2050 to get 237.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2370, and continue the process.

Step 12:
The number 259 fits into 2370 9 times, leaving a remainder of 39.
The number 9 becomes the next digit in our result. 
Result so far: 41086.0579
The remainder is 39 after subtracting 2331 from 2370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

On to step 13:
259 goes into 390 1 times with a remainder of 131.
Record the quotient 1 as the next digit in the result. 
Result so far: 41086.05791
Subtracting 259 from 390 leaves us with 131.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1310, and continue the process.

Going ahead to step 14:
1310 divided by 259 is 5 with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 41086.057915
If we subtract 1295 from 1310, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 15:
259 goes into 150 0 times with a remainder of 150.
Use 0 as the next digit of our solution. 
Result so far: 41086.057915
Subtract 0 from 150 to get 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1500, and continue the process.

Moving on to step 16:
When dividing 1500 by 259, we get 5 with a remainder of 205.
Use 5 as the next digit of our solution. 
Result so far: 41086.05791505
Subtracting 1295 from 1500 leaves us with 205.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2050, and continue the process.

The final result is 41086.05791505 with a remainder of 2.05e-07.