We look at the division of 105251 by 38 
We want to figure out the number of times 105251 can be divided by 38.

Step 1:
When dividing 1 by 38, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 38

Going ahead to step 2:
38 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Include the next digit (5) from the dividend after 10, then repeat: 105 / 38

On to step 3:
The number 38 fits into 105 2 times, leaving a remainder of 29.
Put 2 as the next digit of the answer. 
Result so far: 2.0
The remainder is 29 after subtracting 76 from 105.
Append the next digit (2) from the dividend to 29 and continue with: 292 / 38

Let's proceed to step 4:
The number 38 fits into 292 7 times, leaving a remainder of 26.
Write down 7 as next digit of the result. 
Result so far: 27.0
If we take 266 away from 292, we end up with 26.
Fetch the next digit (5) from the dividend, attach it to 26 and continue: 265 / 38

Moving on to step 5:
The number 38 fits into 265 6 times, leaving a remainder of 37.
The next digit of our result is 6. 
Result so far: 276.0
If we subtract 228 from 265, we get 37.
Append the next digit (1) from the dividend to 37 and continue with: 371 / 38

Moving on to step 6:
371 divided by 38 is 9 with a remainder of 29.
The number 9 becomes the next digit in our result. 
Result so far: 2769.0
The remainder is 29 after subtracting 342 from 371.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 7:
If we divide 290 by 38, we get 7 and a remainder of 24.
Use 7 as the next digit of our solution. 
Result so far: 2769.7
If we take 266 away from 290, we end up 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.

On to step 8:
38 goes into 240 6 times with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 2769.76
Subtract 228 from 240 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 9:
120 divided by 38 is 3 with a remainder of 6.
Write down 3 as next digit of the result. 
Result so far: 2769.763
Subtracting 114 from 120 leaves us 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.

Step 10:
When dividing 60 by 38, we get 1 with a remainder of 22.
Write down 1 as next digit of the result. 
Result so far: 2769.7631
The remainder is 22 after subtracting 38 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 11:
The number 38 fits into 220 5 times, leaving a remainder of 30.
The number 5 becomes the next digit in our result. 
Result so far: 2769.76315
If we take 190 away from 220, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 12:
38 can be fit into 300 7 times, resulting in a remainder of 34.
The number 7 becomes the next digit in our result. 
Result so far: 2769.763157
The remainder is 34 after subtracting 266 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 13:
When dividing 340 by 38, we get 8 with a remainder of 36.
Write down 8 as next digit of the result. 
Result so far: 2769.7631578
If we take 304 away from 340, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 14:
38 can be fit into 360 9 times, resulting in a remainder of 18.
Use 9 as the next digit of our solution. 
Result so far: 2769.76315789
Subtract 342 from 360 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

The quotient of the division is 2769.76315789, and the remainder is 1.8e-08.