We're dividing 338691 by 91 
We're looking to find how many times 91 goes into 338691.

Step 1:
When dividing 3 by 91, we get 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 91

On to step 2:
The number 91 fits into 33 0 times, leaving a remainder of 33.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 33 after subtracting 0 from 33.
Include the next digit (8) from the dividend after 33, then repeat: 338 / 91

Moving on to step 3:
91 can be fit into 338 3 times, resulting in a remainder of 65.
The next digit of our result is 3. 
Result so far: 3.0
Deduct 273 from 338 and we're left with 65.
Include the next digit (6) from the dividend after 65, then repeat: 656 / 91

Going ahead to step 4:
If we divide 656 by 91, we get 7 and a remainder of 19.
Use 7 as the next digit of our solution. 
Result so far: 37.0
Subtracting 637 from 656 leaves us with 19.
Append the next digit (9) from the dividend to 19 and continue with: 199 / 91

Step 5:
When dividing 199 by 91, we get 2 with a remainder of 17.
Record the quotient 2 as the next digit in the result. 
Result so far: 372.0
If we subtract 182 from 199, we get 17.
Take the next digit (1) from the dividend and append it to 17, then repeat: 171 / 91

On to step 6:
91 can be fit into 171 1 times, resulting in a remainder of 80.
Use 1 as the next digit of our solution. 
Result so far: 3721.0
Subtracting 91 from 171 leaves us with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Step 7:
91 can be fit into 800 8 times, resulting in a remainder of 72.
The next digit of our result is 8. 
Result so far: 3721.8
Subtracting 728 from 800 leaves us with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Going ahead to step 8:
When dividing 720 by 91, we get 7 with a remainder of 83.
Use 7 as the next digit of our solution. 
Result so far: 3721.87
If we subtract 637 from 720, we get 83.
Since there are no more digits in the dividend, we add a zero to the remainder making it 830, and continue the process.

Moving on to step 9:
When dividing 830 by 91, we get 9 with a remainder of 11.
Write down 9 as next digit of the result. 
Result so far: 3721.879
If we take 819 away from 830, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 10:
91 goes into 110 1 times with a remainder of 19.
The number 1 becomes the next digit in our result. 
Result so far: 3721.8791
The remainder is 19 after subtracting 91 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Going ahead to step 11:
190 divided by 91 is 2 with a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 3721.87912
The remainder is 8 after subtracting 182 from 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 12:
When dividing 80 by 91, we get 0 with a remainder of 80.
The number 0 becomes the next digit in our result. 
Result so far: 3721.87912
Subtracting 0 from 80 leaves us with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Let's proceed to step 13:
When dividing 800 by 91, we get 8 with a remainder of 72.
Record the quotient 8 as the next digit in the result. 
Result so far: 3721.8791208
If we take 728 away from 800, we end up with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Going ahead to step 14:
The number 91 fits into 720 7 times, leaving a remainder of 83.
Record the quotient 7 as the next digit in the result. 
Result so far: 3721.87912087
Subtracting 637 from 720 leaves us with 83.
Since there are no more digits in the dividend, we add a zero to the remainder making it 830, and continue the process.

The final result is 3721.87912087 with a remainder of 8.3e-08.