We look at the division of 376005 by 9 
We want to figure out the number of times 376005 can be divided by 9.

Let's proceed to step 1:
3 divided by 9 is 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 9

Let's proceed to step 2:
9 goes into 37 4 times with a remainder of 1.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Subtracting 36 from 37 leaves us with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 9

Step 3:
9 goes into 16 1 times with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 41.0
If we subtract 9 from 16, we get 7.
Append the next digit (0) from the dividend to 7 and continue with: 70 / 9

Advancing to step 4:
9 can be fit into 70 7 times, resulting in a remainder of 7.
The next digit of our result is 7. 
Result so far: 417.0
If we take 63 away from 70, we end up with 7.
Append the next digit (0) from the dividend to 7 and continue with: 70 / 9

Let's proceed to step 5:
If we divide 70 by 9, we get 7 and a remainder of 7.
The number 7 becomes the next digit in our result. 
Result so far: 4177.0
If we subtract 63 from 70, we get 7.
Fetch the next digit (5) from the dividend, attach it to 7 and continue: 75 / 9

Step 6:
9 can be fit into 75 8 times, resulting in a remainder of 3.
Put 8 as the next digit of the answer. 
Result so far: 41778.0
If we subtract 72 from 75, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 7:
30 divided by 9 is 3 with a remainder of 3.
The next digit of our result is 3. 
Result so far: 41778.3
The remainder is 3 after subtracting 27 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 8:
The number 9 fits into 30 3 times, leaving a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 41778.33
Subtract 27 from 30 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The quotient of the division is 41778.33, and the remainder is 0.003.