We're dividing 25667 by 13 
We want to figure out the number of times 25667 can be divided by 13.

Let's proceed to step 1:
When dividing 2 by 13, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 13

Going ahead to step 2:
13 goes into 25 1 times with a remainder of 12.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 12 after subtracting 13 from 25.
Include the next digit (6) from the dividend after 12, then repeat: 126 / 13

Going ahead to step 3:
The number 13 fits into 126 9 times, leaving a remainder of 9.
The next digit of our result is 9. 
Result so far: 19.0
Subtracting 117 from 126 leaves us with 9.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 13

Step 4:
96 divided by 13 is 7 with a remainder of 5.
The next digit of our result is 7. 
Result so far: 197.0
The remainder is 5 after subtracting 91 from 96.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 13

Step 5:
13 goes into 57 4 times with a remainder of 5.
Write down 4 as next digit of the result. 
Result so far: 1974.0
Deduct 52 from 57 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.

Going ahead to step 6:
13 goes into 50 3 times with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 1974.3
Deduct 39 from 50 and we're left 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.

Advancing to step 7:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 1974.38
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.

On to step 8:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 1974.384
Deduct 52 from 60 and we're left 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.

Advancing to step 9:
The number 13 fits into 80 6 times, leaving a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 1974.3846
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:
If we divide 20 by 13, we get 1 and a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 1974.38461
Deduct 13 from 20 and we're left 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.

Moving on to step 11:
If we divide 70 by 13, we get 5 and a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 1974.384615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 12:
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: 1974.3846153
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 13:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 1974.38461538
If we take 104 away from 110, we end up 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.

In conclusion, the division gives 1974.38461538 with a balance of 6e-09.