We look at the division of 354219 by 55 
We're looking to find how many times 55 goes into 354219.

Step 1:
55 can be fit into 3 0 times, resulting in a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 55

On to step 2:
55 goes into 35 0 times with a remainder of 35.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 35 after subtracting 0 from 35.
Grab the next digit (4) from the dividend, add it to 35, then carry on: 354 / 55

Moving on to step 3:
If we divide 354 by 55, we get 6 and a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 330 from 354, we get 24.
Grab the next digit (2) from the dividend, add it to 24, then carry on: 242 / 55

Moving on to step 4:
When dividing 242 by 55, we get 4 with a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 64.0
The remainder is 22 after subtracting 220 from 242.
Append the next digit (1) from the dividend to 22 and continue with: 221 / 55

Step 5:
The number 55 fits into 221 4 times, leaving a remainder of 1.
The next digit of our result is 4. 
Result so far: 644.0
If we take 220 away from 221, we end up with 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 55

Moving on to step 6:
55 goes into 19 0 times with a remainder of 19.
Use 0 as the next digit of our solution. 
Result so far: 6440.0
The remainder is 19 after subtracting 0 from 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 7:
55 goes into 190 3 times with a remainder of 25.
Record the quotient 3 as the next digit in the result. 
Result so far: 6440.3
Subtracting 165 from 190 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 8:
55 goes into 250 4 times with a remainder of 30.
Put 4 as the next digit of the answer. 
Result so far: 6440.34
If we take 220 away from 250, 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.

Let's proceed to step 9:
When dividing 300 by 55, we get 5 with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 6440.345
Subtract 275 from 300 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 10:
55 goes into 250 4 times with a remainder of 30.
Put 4 as the next digit of the answer. 
Result so far: 6440.3454
Subtract 220 from 250 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 11:
55 goes into 300 5 times with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 6440.34545
Subtracting 275 from 300 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 12:
55 goes into 250 4 times with a remainder of 30.
The number 4 becomes the next digit in our result. 
Result so far: 6440.345454
Subtract 220 from 250 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 13:
300 divided by 55 is 5 with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 6440.3454545
If we take 275 away from 300, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 14:
The number 55 fits into 250 4 times, leaving a remainder of 30.
The next digit of our result is 4. 
Result so far: 6440.34545454
If we subtract 220 from 250, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The quotient of the division is 6440.34545454, and the remainder is 3e-08.