338896 ÷ 90 
We're looking to find how many times 90 goes into 338896.

Going ahead to step 1:
The number 90 fits into 3 0 times, leaving a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 90

Advancing to step 2:
The number 90 fits into 33 0 times, leaving a remainder of 33.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 33, we end up with 33.
Grab the next digit (8) from the dividend, add it to 33, then carry on: 338 / 90

Advancing to step 3:
If we divide 338 by 90, we get 3 and a remainder of 68.
Put 3 as the next digit of the answer. 
Result so far: 3.0
Deduct 270 from 338 and we're left with 68.
Bring next digit (8) of the dividend behind the 68 and repeat the process: 688 / 90

On to step 4:
The number 90 fits into 688 7 times, leaving a remainder of 58.
The next digit of our result is 7. 
Result so far: 37.0
Subtract 630 from 688 to get 58.
Fetch the next digit (9) from the dividend, attach it to 58 and continue: 589 / 90

Let's proceed to step 5:
90 goes into 589 6 times with a remainder of 49.
Put 6 as the next digit of the answer. 
Result so far: 376.0
The remainder is 49 after subtracting 540 from 589.
Grab the next digit (6) from the dividend, add it to 49, then carry on: 496 / 90

Going ahead to step 6:
496 divided by 90 is 5 with a remainder of 46.
Write down 5 as next digit of the result. 
Result so far: 3765.0
Subtracting 450 from 496 leaves us with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

On to step 7:
90 goes into 460 5 times with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 3765.5
Subtract 450 from 460 to 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 8:
90 can be fit into 100 1 times, resulting in a remainder of 10.
The next digit of our result is 1. 
Result so far: 3765.51
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 9:
90 can be fit into 100 1 times, resulting in a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 3765.511
Subtracting 90 from 100 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 3765.511, and the remainder is 0.001.