We look at the division of 25705825 by 503 
We're looking to find how many times 503 goes into 25705825.

On to step 1:
2 divided by 503 is 0 with a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 503

Advancing to step 2:
When dividing 25 by 503, we get 0 with a remainder of 25.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 25 and we're left with 25.
Include the next digit (7) from the dividend after 25, then repeat: 257 / 503

On to step 3:
503 can be fit into 257 0 times, resulting in a remainder of 257.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 257 and we're left with 257.
Take the next digit (0) from the dividend and append it to 257, then repeat: 2570 / 503

Moving on to step 4:
If we divide 2570 by 503, we get 5 and a remainder of 55.
Write down 5 as next digit of the result. 
Result so far: 5.0
The remainder is 55 after subtracting 2515 from 2570.
Append the next digit (5) from the dividend to 55 and continue with: 555 / 503

Moving on to step 5:
When dividing 555 by 503, we get 1 with a remainder of 52.
Record the quotient 1 as the next digit in the result. 
Result so far: 51.0
Subtracting 503 from 555 leaves us with 52.
Bring next digit (8) of the dividend behind the 52 and repeat the process: 528 / 503

On to step 6:
When dividing 528 by 503, we get 1 with a remainder of 25.
The next digit of our result is 1. 
Result so far: 511.0
If we take 503 away from 528, we end up with 25.
Grab the next digit (2) from the dividend, add it to 25, then carry on: 252 / 503

On to step 7:
503 goes into 252 0 times with a remainder of 252.
Record the quotient 0 as the next digit in the result. 
Result so far: 5110.0
Subtract 0 from 252 to get 252.
Include the next digit (5) from the dividend after 252, then repeat: 2525 / 503

Going ahead to step 8:
When dividing 2525 by 503, we get 5 with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 51105.0
If we subtract 2515 from 2525, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 9:
When dividing 100 by 503, we get 0 with a remainder of 100.
The next digit of our result is 0. 
Result so far: 51105.0
Subtracting 0 from 100 leaves us with 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1000, and continue the process.

Let's proceed to step 10:
If we divide 1000 by 503, we get 1 and a remainder of 497.
Write down 1 as next digit of the result. 
Result so far: 51105.01
If we subtract 503 from 1000, we get 497.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4970, and continue the process.

Step 11:
503 can be fit into 4970 9 times, resulting in a remainder of 443.
The number 9 becomes the next digit in our result. 
Result so far: 51105.019
If we take 4527 away from 4970, we end up with 443.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4430, and continue the process.

Let's proceed to step 12:
4430 divided by 503 is 8 with a remainder of 406.
Use 8 as the next digit of our solution. 
Result so far: 51105.0198
Deduct 4024 from 4430 and we're left with 406.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4060, and continue the process.

Going ahead to step 13:
When dividing 4060 by 503, we get 8 with a remainder of 36.
Record the quotient 8 as the next digit in the result. 
Result so far: 51105.01988
If we subtract 4024 from 4060, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

The quotient of the division is 51105.01988, and the remainder is 3.6e-05.