We look at the division of 4455342 by 371 
Let's see how many times 371 fits into 4455342.

Going ahead to step 1:
371 goes into 4 0 times with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Fetch the next digit (4) from the dividend, attach it to 4 and continue: 44 / 371

Going ahead to step 2:
The number 371 fits into 44 0 times, leaving a remainder of 44.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 44, we get 44.
Grab the next digit (5) from the dividend, add it to 44, then carry on: 445 / 371

Going ahead to step 3:
371 can be fit into 445 1 times, resulting in a remainder of 74.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 371 away from 445, we end up with 74.
Take the next digit (5) from the dividend and append it to 74, then repeat: 745 / 371

Let's proceed to step 4:
371 goes into 745 2 times with a remainder of 3.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Subtract 742 from 745 to get 3.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 371

Advancing to step 5:
371 can be fit into 33 0 times, resulting in a remainder of 33.
Use 0 as the next digit of our solution. 
Result so far: 120.0
If we take 0 away from 33, we end up with 33.
Append the next digit (4) from the dividend to 33 and continue with: 334 / 371

Step 6:
371 can be fit into 334 0 times, resulting in a remainder of 334.
Write down 0 as next digit of the result. 
Result so far: 1200.0
If we subtract 0 from 334, we get 334.
Grab the next digit (2) from the dividend, add it to 334, then carry on: 3342 / 371

Going ahead to step 7:
371 can be fit into 3342 9 times, resulting in a remainder of 3.
The next digit of our result is 9. 
Result so far: 12009.0
If we take 3339 away from 3342, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 8:
If we divide 30 by 371, we get 0 and a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 12009.0
If we take 0 away from 30, 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.

Advancing to step 9:
The number 371 fits into 300 0 times, leaving a remainder of 300.
Put 0 as the next digit of the answer. 
Result so far: 12009.0
Subtracting 0 from 300 leaves us with 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3000, and continue the process.

The quotient of the division is 12009.0, and the remainder is 0.3.