We're dividing 25290874 by 827 
We're looking to find how many times 827 goes into 25290874.

Going ahead to step 1:
When dividing 2 by 827, we get 0 with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 827

On to step 2:
The number 827 fits into 25 0 times, leaving a remainder of 25.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 25, we end up with 25.
Take the next digit (2) from the dividend and append it to 25, then repeat: 252 / 827

Moving on to step 3:
The number 827 fits into 252 0 times, leaving a remainder of 252.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 252, we get 252.
Grab the next digit (9) from the dividend, add it to 252, then carry on: 2529 / 827

Step 4:
827 goes into 2529 3 times with a remainder of 48.
Put 3 as the next digit of the answer. 
Result so far: 3.0
Deduct 2481 from 2529 and we're left with 48.
Fetch the next digit (0) from the dividend, attach it to 48 and continue: 480 / 827

Let's proceed to step 5:
480 divided by 827 is 0 with a remainder of 480.
Record the quotient 0 as the next digit in the result. 
Result so far: 30.0
Subtracting 0 from 480 leaves us with 480.
Take the next digit (8) from the dividend and append it to 480, then repeat: 4808 / 827

Moving on to step 6:
4808 divided by 827 is 5 with a remainder of 673.
Put 5 as the next digit of the answer. 
Result so far: 305.0
Deduct 4135 from 4808 and we're left with 673.
Include the next digit (7) from the dividend after 673, then repeat: 6737 / 827

Advancing to step 7:
If we divide 6737 by 827, we get 8 and a remainder of 121.
The number 8 becomes the next digit in our result. 
Result so far: 3058.0
Subtract 6616 from 6737 to get 121.
Fetch the next digit (4) from the dividend, attach it to 121 and continue: 1214 / 827

Advancing to step 8:
827 goes into 1214 1 times with a remainder of 387.
The next digit of our result is 1. 
Result so far: 30581.0
The remainder is 387 after subtracting 827 from 1214.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3870, and continue the process.

Moving on to step 9:
When dividing 3870 by 827, we get 4 with a remainder of 562.
The next digit of our result is 4. 
Result so far: 30581.4
Subtract 3308 from 3870 to get 562.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5620, and continue the process.

Let's proceed to step 10:
If we divide 5620 by 827, we get 6 and a remainder of 658.
Put 6 as the next digit of the answer. 
Result so far: 30581.46
If we take 4962 away from 5620, we end up with 658.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6580, and continue the process.

Moving on to step 11:
827 can be fit into 6580 7 times, resulting in a remainder of 791.
The number 7 becomes the next digit in our result. 
Result so far: 30581.467
Deduct 5789 from 6580 and we're left with 791.
Since there are no more digits in the dividend, we add a zero to the remainder making it 7910, and continue the process.

Going ahead to step 12:
827 goes into 7910 9 times with a remainder of 467.
Put 9 as the next digit of the answer. 
Result so far: 30581.4679
Subtracting 7443 from 7910 leaves us with 467.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4670, and continue the process.

Advancing to step 13:
The number 827 fits into 4670 5 times, leaving a remainder of 535.
The next digit of our result is 5. 
Result so far: 30581.46795
If we subtract 4135 from 4670, we get 535.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5350, and continue the process.

Step 14:
The number 827 fits into 5350 6 times, leaving a remainder of 388.
The next digit of our result is 6. 
Result so far: 30581.467956
Subtract 4962 from 5350 to get 388.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3880, and continue the process.

On to step 15:
When dividing 3880 by 827, we get 4 with a remainder of 572.
Use 4 as the next digit of our solution. 
Result so far: 30581.4679564
Deduct 3308 from 3880 and we're left with 572.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5720, and continue the process.

Going ahead to step 16:
827 goes into 5720 6 times with a remainder of 758.
Record the quotient 6 as the next digit in the result. 
Result so far: 30581.46795646
Subtract 4962 from 5720 to 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.

Our division results in 30581.46795646 with a remaining 7.58e-07.