338925 ÷ 90 
We're looking to find how many times 90 goes into 338925.

On to step 1:
If we divide 3 by 90, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 90

Advancing to step 2:
If we divide 33 by 90, we get 0 and a remainder of 33.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 33 to get 33.
Append the next digit (8) from the dividend to 33 and continue with: 338 / 90

Moving on to step 3:
90 goes into 338 3 times with a remainder of 68.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
If we subtract 270 from 338, we get 68.
Fetch the next digit (9) from the dividend, attach it to 68 and continue: 689 / 90

Step 4:
When dividing 689 by 90, we get 7 with a remainder of 59.
Write down 7 as next digit of the result. 
Result so far: 37.0
The remainder is 59 after subtracting 630 from 689.
Grab the next digit (2) from the dividend, add it to 59, then carry on: 592 / 90

On to step 5:
90 can be fit into 592 6 times, resulting in a remainder of 52.
Record the quotient 6 as the next digit in the result. 
Result so far: 376.0
Subtracting 540 from 592 leaves us with 52.
Bring next digit (5) of the dividend behind the 52 and repeat the process: 525 / 90

Going ahead to step 6:
When dividing 525 by 90, we get 5 with a remainder of 75.
Write down 5 as next digit of the result. 
Result so far: 3765.0
The remainder is 75 after subtracting 450 from 525.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Moving on to step 7:
If we divide 750 by 90, we get 8 and a remainder of 30.
Put 8 as the next digit of the answer. 
Result so far: 3765.8
Subtract 720 from 750 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 8:
The number 90 fits into 300 3 times, leaving a remainder of 30.
Use 3 as the next digit of our solution. 
Result so far: 3765.83
Subtract 270 from 300 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 9:
The number 90 fits into 300 3 times, leaving a remainder of 30.
Use 3 as the next digit of our solution. 
Result so far: 3765.833
Deduct 270 from 300 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The quotient of the division is 3765.833, and the remainder is 0.003.