2266 ÷ 7 
We want to figure out the number of times 2266 can be divided by 7.

Advancing to step 1:
When dividing 2 by 7, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Fetch the next digit (2) from the dividend, attach it to 2 and continue: 22 / 7

Step 2:
When dividing 22 by 7, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 3.0
Subtracting 21 from 22 leaves us with 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 7

Going ahead to step 3:
16 divided by 7 is 2 with a remainder of 2.
The next digit of our result is 2. 
Result so far: 32.0
Subtracting 14 from 16 leaves us with 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 7

Moving on to step 4:
26 divided by 7 is 3 with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 323.0
Subtract 21 from 26 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 5:
When dividing 50 by 7, we get 7 with a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 323.7
Subtract 49 from 50 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 6:
10 divided by 7 is 1 with a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 323.71
Subtract 7 from 10 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 7:
When dividing 30 by 7, we get 4 with a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 323.714
Subtract 28 from 30 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 8:
The number 7 fits into 20 2 times, leaving a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 323.7142
Subtracting 14 from 20 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 9:
When dividing 60 by 7, we get 8 with a remainder of 4.
The next digit of our result is 8. 
Result so far: 323.71428
If we take 56 away from 60, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 10:
If we divide 40 by 7, we get 5 and a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 323.714285
If we subtract 35 from 40, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 11:
7 goes into 50 7 times with a remainder of 1.
The next digit of our result is 7. 
Result so far: 323.7142857
The remainder is 1 after subtracting 49 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 12:
7 goes into 10 1 times with a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 323.71428571
The remainder is 3 after subtracting 7 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The final outcome is 323.71428571, with a leftover of 3e-09.