We divide 100646 by 13
We want to figure out the number of times 100646 can be divided by 13.

Moving on to step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 13

Advancing to step 2:
10 divided by 13 is 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Bring next digit (0) of the dividend behind the 10 and repeat the process: 100 / 13

Step 3:
If we divide 100 by 13, we get 7 and a remainder of 9.
The next digit of our result is 7. 
Result so far: 7.0
The remainder is 9 after subtracting 91 from 100.
Bring next digit (6) of the dividend behind the 9 and repeat the process: 96 / 13

Moving on to step 4:
When dividing 96 by 13, we get 7 with a remainder of 5.
Put 7 as the next digit of the answer. 
Result so far: 77.0
Deduct 91 from 96 and we're left with 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 13

Moving on to step 5:
If we divide 54 by 13, we get 4 and a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 774.0
The remainder is 2 after subtracting 52 from 54.
Take the next digit (6) from the dividend and append it to 2, then repeat: 26 / 13

Step 6:
26 divided by 13 is 2 with a remainder of 0.
Put 2 as the next digit of the answer. 
Result so far: 7742.0
If we subtract 26 from 26, 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.

On to step 7:
13 goes into 0 0 times with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 7742.0
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.

Moving on to step 8:
13 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 7742.0
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.

Our division results in 7742.0 with a remaining 0.0.