7508227 ÷ 338 
We're looking to find how many times 338 goes into 7508227.

Let's proceed to step 1:
If we divide 7 by 338, we get 0 and a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 338

Advancing to step 2:
If we divide 75 by 338, we get 0 and a remainder of 75.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 75, we get 75.
Grab the next digit (0) from the dividend, add it to 75, then carry on: 750 / 338

Going ahead to step 3:
When dividing 750 by 338, we get 2 with a remainder of 74.
Write down 2 as next digit of the result. 
Result so far: 2.0
Subtracting 676 from 750 leaves us with 74.
Bring next digit (8) of the dividend behind the 74 and repeat the process: 748 / 338

Let's proceed to step 4:
338 goes into 748 2 times with a remainder of 72.
Write down 2 as next digit of the result. 
Result so far: 22.0
Subtract 676 from 748 to get 72.
Grab the next digit (2) from the dividend, add it to 72, then carry on: 722 / 338

Advancing to step 5:
When dividing 722 by 338, we get 2 with a remainder of 46.
Put 2 as the next digit of the answer. 
Result so far: 222.0
Deduct 676 from 722 and we're left with 46.
Include the next digit (2) from the dividend after 46, then repeat: 462 / 338

Going ahead to step 6:
462 divided by 338 is 1 with a remainder of 124.
Put 1 as the next digit of the answer. 
Result so far: 2221.0
Deduct 338 from 462 and we're left with 124.
Append the next digit (7) from the dividend to 124 and continue with: 1247 / 338

On to step 7:
1247 divided by 338 is 3 with a remainder of 233.
The next digit of our result is 3. 
Result so far: 22213.0
The remainder is 233 after subtracting 1014 from 1247.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2330, and continue the process.

Advancing to step 8:
The number 338 fits into 2330 6 times, leaving a remainder of 302.
The next digit of our result is 6. 
Result so far: 22213.6
Subtract 2028 from 2330 to get 302.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3020, and continue the process.

Going ahead to step 9:
338 goes into 3020 8 times with a remainder of 316.
Use 8 as the next digit of our solution. 
Result so far: 22213.68
Subtracting 2704 from 3020 leaves us with 316.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3160, and continue the process.

Step 10:
3160 divided by 338 is 9 with a remainder of 118.
Record the quotient 9 as the next digit in the result. 
Result so far: 22213.689
If we subtract 3042 from 3160, we get 118.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1180, and continue the process.

On to step 11:
338 can be fit into 1180 3 times, resulting in a remainder of 166.
Write down 3 as next digit of the result. 
Result so far: 22213.6893
If we take 1014 away from 1180, we end up with 166.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1660, and continue the process.

Step 12:
1660 divided by 338 is 4 with a remainder of 308.
Write down 4 as next digit of the result. 
Result so far: 22213.68934
If we take 1352 away from 1660, we end up with 308.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3080, and continue the process.

Moving on to step 13:
The number 338 fits into 3080 9 times, leaving a remainder of 38.
The next digit of our result is 9. 
Result so far: 22213.689349
Subtracting 3042 from 3080 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Moving on to step 14:
380 divided by 338 is 1 with a remainder of 42.
The next digit of our result is 1. 
Result so far: 22213.6893491
If we take 338 away from 380, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Going ahead to step 15:
338 goes into 420 1 times with a remainder of 82.
The number 1 becomes the next digit in our result. 
Result so far: 22213.68934911
Subtract 338 from 420 to get 82.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

After the division, we end up with 22213.68934911 and a remainder of 8.2e-08.