We look at the division of 10946 by 13 
Let's see how many times 13 fits into 10946.

Going ahead to step 1:
When dividing 1 by 13, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 13

Advancing to step 2:
10 divided by 13 is 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 13

Advancing to step 3:
13 goes into 109 8 times with a remainder of 5.
The next digit of our result is 8. 
Result so far: 8.0
Subtracting 104 from 109 leaves us with 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 13

Moving on to step 4:
54 divided by 13 is 4 with a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 84.0
Subtract 52 from 54 to get 2.
Include the next digit (6) from the dividend after 2, then repeat: 26 / 13

Going ahead to step 5:
13 goes into 26 2 times with a remainder of 0.
Record the quotient 2 as the next digit in the result. 
Result so far: 842.0
If we take 26 away from 26, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 6:
The number 13 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 842.0
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 7:
If we divide 0 by 13, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 842.0
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

After the division, we end up with 842.0 and a remainder of 0.0.