We look at the division of 376569 by 38 
Our goal is to divide 376569 by 38.

Advancing to step 1:
If we divide 3 by 38, we get 0 and a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 38

Moving on to step 2:
When dividing 37 by 38, we get 0 with a remainder of 37.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Append the next digit (6) from the dividend to 37 and continue with: 376 / 38

Let's proceed to step 3:
38 can be fit into 376 9 times, resulting in a remainder of 34.
Put 9 as the next digit of the answer. 
Result so far: 9.0
If we take 342 away from 376, we end up with 34.
Include the next digit (5) from the dividend after 34, then repeat: 345 / 38

On to step 4:
When dividing 345 by 38, we get 9 with a remainder of 3.
The next digit of our result is 9. 
Result so far: 99.0
Deduct 342 from 345 and we're left with 3.
Fetch the next digit (6) from the dividend, attach it to 3 and continue: 36 / 38

Let's proceed to step 5:
36 divided by 38 is 0 with a remainder of 36.
The number 0 becomes the next digit in our result. 
Result so far: 990.0
If we take 0 away from 36, we end up with 36.
Append the next digit (9) from the dividend to 36 and continue with: 369 / 38

Let's proceed to step 6:
369 divided by 38 is 9 with a remainder of 27.
Put 9 as the next digit of the answer. 
Result so far: 9909.0
Subtract 342 from 369 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Going ahead to step 7:
270 divided by 38 is 7 with a remainder of 4.
Write down 7 as next digit of the result. 
Result so far: 9909.7
If we subtract 266 from 270, 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.

Going ahead to step 8:
38 goes into 40 1 times with a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 9909.71
If we subtract 38 from 40, we 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.

On to step 9:
If we divide 20 by 38, we get 0 and a remainder of 20.
Write down 0 as next digit of the result. 
Result so far: 9909.71
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 10:
38 can be fit into 200 5 times, resulting in a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 9909.7105
The remainder is 10 after subtracting 190 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 11:
38 goes into 100 2 times with a remainder of 24.
Use 2 as the next digit of our solution. 
Result so far: 9909.71052
If we subtract 76 from 100, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 12:
If we divide 240 by 38, we get 6 and a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 9909.710526
The remainder is 12 after subtracting 228 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 13:
The number 38 fits into 120 3 times, leaving a remainder of 6.
The next digit of our result is 3. 
Result so far: 9909.7105263
Subtract 114 from 120 to 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.

Let's proceed to step 14:
When dividing 60 by 38, we get 1 with a remainder of 22.
Record the quotient 1 as the next digit in the result. 
Result so far: 9909.71052631
Deduct 38 from 60 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

The quotient of the division is 9909.71052631, and the remainder is 2.2e-08.