We're dividing 679105 by 13 
Let's see how many times 13 fits into 679105.

Going ahead to step 1:
The number 13 fits into 6 0 times, leaving a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 13

Step 2:
When dividing 67 by 13, we get 5 with a remainder of 2.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we take 65 away from 67, we end up with 2.
Fetch the next digit (9) from the dividend, attach it to 2 and continue: 29 / 13

Advancing to step 3:
13 can be fit into 29 2 times, resulting in a remainder of 3.
The number 2 becomes the next digit in our result. 
Result so far: 52.0
If we take 26 away from 29, we end up with 3.
Include the next digit (1) from the dividend after 3, then repeat: 31 / 13

Going ahead to step 4:
31 divided by 13 is 2 with a remainder of 5.
The next digit of our result is 2. 
Result so far: 522.0
If we subtract 26 from 31, we get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 13

Let's proceed to step 5:
If we divide 50 by 13, we get 3 and a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 5223.0
If we subtract 39 from 50, we get 11.
Grab the next digit (5) from the dividend, add it to 11, then carry on: 115 / 13

Advancing to step 6:
115 divided by 13 is 8 with a remainder of 11.
Put 8 as the next digit of the answer. 
Result so far: 52238.0
The remainder is 11 after subtracting 104 from 115.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 7:
110 divided by 13 is 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 52238.8
Subtracting 104 from 110 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.

Advancing to step 8:
When dividing 60 by 13, we get 4 with a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 52238.84
Subtracting 52 from 60 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 9:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 52238.846
Deduct 78 from 80 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 10:
When dividing 20 by 13, we get 1 with a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 52238.8461
If we take 13 away from 20, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 11:
When dividing 70 by 13, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 52238.84615
Subtract 65 from 70 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.

Let's proceed to step 12:
13 goes into 50 3 times with a remainder of 11.
The next digit of our result is 3. 
Result so far: 52238.846153
Subtracting 39 from 50 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 13:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 52238.8461538
Subtract 104 from 110 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 14:
60 divided by 13 is 4 with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 52238.84615384
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The quotient of the division is 52238.84615384, and the remainder is 8e-09.