Let's divide 100674 by 13
Our goal is to divide 100674 by 13.

Advancing to step 1:
When dividing 1 by 13, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 13

Going ahead to step 2:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Fetch the next digit (0) from the dividend, attach it to 10 and continue: 100 / 13

Let's proceed to 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
If we subtract 91 from 100, we get 9.
Bring next digit (6) of the dividend behind the 9 and repeat the process: 96 / 13

Advancing to step 4:
13 can be fit into 96 7 times, resulting in a remainder of 5.
The number 7 becomes the next digit in our result. 
Result so far: 77.0
Subtract 91 from 96 to get 5.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 13

Going ahead to step 5:
57 divided by 13 is 4 with a remainder of 5.
Use 4 as the next digit of our solution. 
Result so far: 774.0
Subtracting 52 from 57 leaves us with 5.
Take the next digit (4) from the dividend and append it to 5, then repeat: 54 / 13

Let's proceed to step 6:
If we divide 54 by 13, we get 4 and a remainder of 2.
Use 4 as the next digit of our solution. 
Result so far: 7744.0
Deduct 52 from 54 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 7:
20 divided by 13 is 1 with a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 7744.1
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 8:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 7744.15
Subtracting 65 from 70 leaves us with 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 9:
13 can be fit into 50 3 times, resulting in a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 7744.153
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 10:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 7744.1538
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 11:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 7744.15384
Subtract 52 from 60 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 12:
If we divide 80 by 13, we get 6 and a remainder of 2.
The next digit of our result is 6. 
Result so far: 7744.153846
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.

Advancing to step 13:
13 goes into 20 1 times with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 7744.1538461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 14:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 7744.15384615
Deduct 65 from 70 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

After the division, we end up with 7744.15384615 and a remainder of 5e-09.