We divide 35679 by 13
We want to figure out the number of times 35679 can be divided by 13.

Moving on to step 1:
The number 13 fits into 3 0 times, leaving a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 13

Advancing to step 2:
13 can be fit into 35 2 times, resulting in a remainder of 9.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Deduct 26 from 35 and we're left with 9.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 13

Moving on to step 3:
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: 27.0
If we subtract 91 from 96, we get 5.
Include the next digit (7) from the dividend after 5, then repeat: 57 / 13

Moving on to step 4:
13 can be fit into 57 4 times, resulting in a remainder of 5.
The number 4 becomes the next digit in our result. 
Result so far: 274.0
Deduct 52 from 57 and we're left with 5.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 13

Going ahead to step 5:
59 divided by 13 is 4 with a remainder of 7.
Put 4 as the next digit of the answer. 
Result so far: 2744.0
The remainder is 7 after subtracting 52 from 59.
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 6:
70 divided by 13 is 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 2744.5
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.

Advancing to step 7:
13 goes into 50 3 times with a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 2744.53
If we take 39 away from 50, we end up 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.

On to step 8:
If we divide 110 by 13, we get 8 and a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 2744.538
If we subtract 104 from 110, we 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 9:
If we divide 60 by 13, we get 4 and a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 2744.5384
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.

Going ahead to step 10:
The number 13 fits into 80 6 times, leaving a remainder of 2.
The next digit of our result is 6. 
Result so far: 2744.53846
Subtract 78 from 80 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 11:
13 can be fit into 20 1 times, resulting in a remainder of 7.
The next digit of our result is 1. 
Result so far: 2744.538461
If we subtract 13 from 20, we 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.

Step 12:
70 divided by 13 is 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 2744.5384615
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.

Moving on to step 13:
If we divide 50 by 13, we get 3 and a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 2744.53846153
If we take 39 away from 50, we end up 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.

After the division, we end up with 2744.53846153 and a remainder of 1.1e-08.