We look at the division of 25961 by 38 
We want to divide 25961 by 38.

Advancing to step 1:
2 divided by 38 is 0 with a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 38

Step 2:
38 goes into 25 0 times with a remainder of 25.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 25, we end up with 25.
Fetch the next digit (9) from the dividend, attach it to 25 and continue: 259 / 38

Let's proceed to step 3:
The number 38 fits into 259 6 times, leaving a remainder of 31.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Subtract 228 from 259 to get 31.
Take the next digit (6) from the dividend and append it to 31, then repeat: 316 / 38

Advancing to step 4:
When dividing 316 by 38, we get 8 with a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 68.0
If we subtract 304 from 316, we get 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 38

Moving on to step 5:
38 goes into 121 3 times with a remainder of 7.
The next digit of our result is 3. 
Result so far: 683.0
The remainder is 7 after subtracting 114 from 121.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 6:
The number 38 fits into 70 1 times, leaving a remainder of 32.
Write down 1 as next digit of the result. 
Result so far: 683.1
If we take 38 away from 70, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 7:
38 goes into 320 8 times with a remainder of 16.
The number 8 becomes the next digit in our result. 
Result so far: 683.18
Deduct 304 from 320 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 8:
160 divided by 38 is 4 with a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 683.184
Deduct 152 from 160 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.

Step 9:
38 can be fit into 80 2 times, resulting in a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 683.1842
If we subtract 76 from 80, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 10:
The number 38 fits into 40 1 times, leaving a remainder of 2.
The next digit of our result is 1. 
Result so far: 683.18421
Subtract 38 from 40 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:
When dividing 20 by 38, we get 0 with a remainder of 20.
The next digit of our result is 0. 
Result so far: 683.18421
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 12:
When dividing 200 by 38, we get 5 with a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 683.1842105
Deduct 190 from 200 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 13:
100 divided by 38 is 2 with a remainder of 24.
Use 2 as the next digit of our solution. 
Result so far: 683.18421052
Subtracting 76 from 100 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Our division results in 683.18421052 with a remaining 2.4e-08.