25813 ÷ 38 
We want to divide 25813 by 38.

Moving on to step 1:
38 goes into 2 0 times with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 38

Let's proceed to step 2:
When dividing 25 by 38, we get 0 with a remainder of 25.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 25 to get 25.
Fetch the next digit (8) from the dividend, attach it to 25 and continue: 258 / 38

Step 3:
38 can be fit into 258 6 times, resulting in a remainder of 30.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 228 from 258 and we're left with 30.
Bring next digit (1) of the dividend behind the 30 and repeat the process: 301 / 38

On to step 4:
When dividing 301 by 38, we get 7 with a remainder of 35.
The next digit of our result is 7. 
Result so far: 67.0
If we subtract 266 from 301, we get 35.
Grab the next digit (3) from the dividend, add it to 35, then carry on: 353 / 38

On to step 5:
38 goes into 353 9 times with a remainder of 11.
Write down 9 as next digit of the result. 
Result so far: 679.0
Deduct 342 from 353 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.

Step 6:
When dividing 110 by 38, we get 2 with a remainder of 34.
Put 2 as the next digit of the answer. 
Result so far: 679.2
Deduct 76 from 110 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 7:
38 can be fit into 340 8 times, resulting in a remainder of 36.
The next digit of our result is 8. 
Result so far: 679.28
Subtract 304 from 340 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 8:
When dividing 360 by 38, we get 9 with a remainder of 18.
The next digit of our result is 9. 
Result so far: 679.289
If we take 342 away from 360, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 9:
The number 38 fits into 180 4 times, leaving a remainder of 28.
Record the quotient 4 as the next digit in the result. 
Result so far: 679.2894
The remainder is 28 after subtracting 152 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 10:
When dividing 280 by 38, we get 7 with a remainder of 14.
Write down 7 as next digit of the result. 
Result so far: 679.28947
Deduct 266 from 280 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 11:
When dividing 140 by 38, we get 3 with a remainder of 26.
Put 3 as the next digit of the answer. 
Result so far: 679.289473
Deduct 114 from 140 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 12:
The number 38 fits into 260 6 times, leaving a remainder of 32.
Use 6 as the next digit of our solution. 
Result so far: 679.2894736
If we subtract 228 from 260, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 13:
320 divided by 38 is 8 with a remainder of 16.
Put 8 as the next digit of the answer. 
Result so far: 679.28947368
Subtracting 304 from 320 leaves us 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.

After the division, we end up with 679.28947368 and a remainder of 1.6e-08.