We look at the division of 371406 by 9 
We want to divide 371406 by 9.

Step 1:
When dividing 3 by 9, we get 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 9

On 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
If we take 36 away from 37, we end up with 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 9

Step 3:
If we divide 11 by 9, we get 1 and a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 41.0
Subtract 9 from 11 to get 2.
Fetch the next digit (4) from the dividend, attach it to 2 and continue: 24 / 9

Let's proceed to step 4:
9 can be fit into 24 2 times, resulting in a remainder of 6.
Write down 2 as next digit of the result. 
Result so far: 412.0
Subtract 18 from 24 to get 6.
Append the next digit (0) from the dividend to 6 and continue with: 60 / 9

Advancing to step 5:
9 can be fit into 60 6 times, resulting in a remainder of 6.
The next digit of our result is 6. 
Result so far: 4126.0
The remainder is 6 after subtracting 54 from 60.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 9

On to step 6:
The number 9 fits into 66 7 times, leaving a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 41267.0
Subtract 63 from 66 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.

Step 7:
9 goes into 30 3 times with a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 41267.3
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.

Going ahead to step 8:
When dividing 30 by 9, we get 3 with a remainder of 3.
The next digit of our result is 3. 
Result so far: 41267.33
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.

The quotient of the division is 41267.33, and the remainder is 0.003.