We look at the division of 17825174 by 480 
Our goal is to divide 17825174 by 480.

Step 1:
When dividing 1 by 480, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 480

Advancing to step 2:
480 can be fit into 17 0 times, resulting in a remainder of 17.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 17 and we're left with 17.
Include the next digit (8) from the dividend after 17, then repeat: 178 / 480

Step 3:
The number 480 fits into 178 0 times, leaving a remainder of 178.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 178 leaves us with 178.
Grab the next digit (2) from the dividend, add it to 178, then carry on: 1782 / 480

On to step 4:
If we divide 1782 by 480, we get 3 and a remainder of 342.
The next digit of our result is 3. 
Result so far: 3.0
Deduct 1440 from 1782 and we're left with 342.
Grab the next digit (5) from the dividend, add it to 342, then carry on: 3425 / 480

Step 5:
480 can be fit into 3425 7 times, resulting in a remainder of 65.
The next digit of our result is 7. 
Result so far: 37.0
The remainder is 65 after subtracting 3360 from 3425.
Include the next digit (1) from the dividend after 65, then repeat: 651 / 480

Step 6:
651 divided by 480 is 1 with a remainder of 171.
Put 1 as the next digit of the answer. 
Result so far: 371.0
If we subtract 480 from 651, we get 171.
Bring next digit (7) of the dividend behind the 171 and repeat the process: 1717 / 480

On to step 7:
480 can be fit into 1717 3 times, resulting in a remainder of 277.
The next digit of our result is 3. 
Result so far: 3713.0
If we subtract 1440 from 1717, we get 277.
Grab the next digit (4) from the dividend, add it to 277, then carry on: 2774 / 480

Advancing to step 8:
2774 divided by 480 is 5 with a remainder of 374.
Use 5 as the next digit of our solution. 
Result so far: 37135.0
Deduct 2400 from 2774 and we're left with 374.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3740, and continue the process.

Let's proceed to step 9:
When dividing 3740 by 480, we get 7 with a remainder of 380.
The number 7 becomes the next digit in our result. 
Result so far: 37135.7
Subtract 3360 from 3740 to get 380.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3800, and continue the process.

Going ahead to step 10:
480 goes into 3800 7 times with a remainder of 440.
The number 7 becomes the next digit in our result. 
Result so far: 37135.77
The remainder is 440 after subtracting 3360 from 3800.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4400, and continue the process.

The quotient of the division is 37135.77, and the remainder is 0.44.