6966 ÷ 23 
We want to figure out the number of times 6966 can be divided by 23.

Moving on to step 1:
23 goes into 6 0 times with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Include the next digit (9) from the dividend after 6, then repeat: 69 / 23

Let's proceed to step 2:
When dividing 69 by 23, we get 3 with a remainder of 0.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Deduct 69 from 69 and we're left with 0.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 23

Going ahead to step 3:
6 divided by 23 is 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 30.0
Subtracting 0 from 6 leaves us with 6.
Append the next digit (6) from the dividend to 6 and continue with: 66 / 23

On to step 4:
The number 23 fits into 66 2 times, leaving a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 302.0
Subtracting 46 from 66 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 5:
When dividing 200 by 23, we get 8 with a remainder of 16.
Write down 8 as next digit of the result. 
Result so far: 302.8
If we take 184 away from 200, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 6:
If we divide 160 by 23, we get 6 and a remainder of 22.
Put 6 as the next digit of the answer. 
Result so far: 302.86
Deduct 138 from 160 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 7:
23 can be fit into 220 9 times, resulting in a remainder of 13.
Use 9 as the next digit of our solution. 
Result so far: 302.869
Deduct 207 from 220 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 8:
23 can be fit into 130 5 times, resulting in a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 302.8695
Deduct 115 from 130 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 9:
150 divided by 23 is 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 302.86956
Subtracting 138 from 150 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 10:
120 divided by 23 is 5 with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 302.869565
The remainder is 5 after subtracting 115 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 11:
23 goes into 50 2 times with a remainder of 4.
The next digit of our result is 2. 
Result so far: 302.8695652
The remainder is 4 after subtracting 46 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 12:
When dividing 40 by 23, we get 1 with a remainder of 17.
The number 1 becomes the next digit in our result. 
Result so far: 302.86956521
Deduct 23 from 40 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

After the division, we end up with 302.86956521 and a remainder of 1.7e-08.