25508253 ÷ 353 
We want to figure out the number of times 25508253 can be divided by 353.

Going ahead to step 1:
When dividing 2 by 353, we get 0 with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 353

Going ahead to step 2:
353 goes into 25 0 times with a remainder of 25.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 25, we end up with 25.
Include the next digit (5) from the dividend after 25, then repeat: 255 / 353

Advancing to step 3:
353 goes into 255 0 times with a remainder of 255.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 255, we end up with 255.
Grab the next digit (0) from the dividend, add it to 255, then carry on: 2550 / 353

Advancing to step 4:
353 can be fit into 2550 7 times, resulting in a remainder of 79.
Write down 7 as next digit of the result. 
Result so far: 7.0
If we take 2471 away from 2550, we end up with 79.
Append the next digit (8) from the dividend to 79 and continue with: 798 / 353

Advancing to step 5:
The number 353 fits into 798 2 times, leaving a remainder of 92.
Record the quotient 2 as the next digit in the result. 
Result so far: 72.0
Deduct 706 from 798 and we're left with 92.
Fetch the next digit (2) from the dividend, attach it to 92 and continue: 922 / 353

Step 6:
The number 353 fits into 922 2 times, leaving a remainder of 216.
Use 2 as the next digit of our solution. 
Result so far: 722.0
The remainder is 216 after subtracting 706 from 922.
Append the next digit (5) from the dividend to 216 and continue with: 2165 / 353

On to step 7:
353 can be fit into 2165 6 times, resulting in a remainder of 47.
Use 6 as the next digit of our solution. 
Result so far: 7226.0
If we subtract 2118 from 2165, we get 47.
Include the next digit (3) from the dividend after 47, then repeat: 473 / 353

Step 8:
353 can be fit into 473 1 times, resulting in a remainder of 120.
The number 1 becomes the next digit in our result. 
Result so far: 72261.0
Subtracting 353 from 473 leaves us with 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1200, and continue the process.

Step 9:
The number 353 fits into 1200 3 times, leaving a remainder of 141.
Use 3 as the next digit of our solution. 
Result so far: 72261.3
Deduct 1059 from 1200 and we're left with 141.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1410, and continue the process.

Step 10:
The number 353 fits into 1410 3 times, leaving a remainder of 351.
Write down 3 as next digit of the result. 
Result so far: 72261.33
The remainder is 351 after subtracting 1059 from 1410.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3510, and continue the process.

The quotient of the division is 72261.33, and the remainder is 0.351.