We're dividing 19188421 by 353 
We want to figure out the number of times 19188421 can be divided by 353.

Step 1:
When dividing 1 by 353, we get 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (9) from the dividend, add it to 1, then carry on: 19 / 353

Advancing to step 2:
When dividing 19 by 353, we get 0 with a remainder of 19.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 19 after subtracting 0 from 19.
Include the next digit (1) from the dividend after 19, then repeat: 191 / 353

On to step 3:
191 divided by 353 is 0 with a remainder of 191.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 191, we end up with 191.
Grab the next digit (8) from the dividend, add it to 191, then carry on: 1918 / 353

Advancing to step 4:
353 can be fit into 1918 5 times, resulting in a remainder of 153.
Write down 5 as next digit of the result. 
Result so far: 5.0
Deduct 1765 from 1918 and we're left with 153.
Fetch the next digit (8) from the dividend, attach it to 153 and continue: 1538 / 353

Going ahead to step 5:
If we divide 1538 by 353, we get 4 and a remainder of 126.
Use 4 as the next digit of our solution. 
Result so far: 54.0
Deduct 1412 from 1538 and we're left with 126.
Include the next digit (4) from the dividend after 126, then repeat: 1264 / 353

Step 6:
1264 divided by 353 is 3 with a remainder of 205.
The number 3 becomes the next digit in our result. 
Result so far: 543.0
If we subtract 1059 from 1264, we get 205.
Append the next digit (2) from the dividend to 205 and continue with: 2052 / 353

Going ahead to step 7:
If we divide 2052 by 353, we get 5 and a remainder of 287.
The number 5 becomes the next digit in our result. 
Result so far: 5435.0
Subtracting 1765 from 2052 leaves us with 287.
Grab the next digit (1) from the dividend, add it to 287, then carry on: 2871 / 353

On to step 8:
The number 353 fits into 2871 8 times, leaving a remainder of 47.
The next digit of our result is 8. 
Result so far: 54358.0
If we subtract 2824 from 2871, we get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

On to step 9:
If we divide 470 by 353, we get 1 and a remainder of 117.
The next digit of our result is 1. 
Result so far: 54358.1
Subtract 353 from 470 to get 117.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1170, and continue the process.

Going ahead to step 10:
If we divide 1170 by 353, we get 3 and a remainder of 111.
Write down 3 as next digit of the result. 
Result so far: 54358.13
Deduct 1059 from 1170 and we're left with 111.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1110, and continue the process.

Let's proceed to step 11:
353 goes into 1110 3 times with a remainder of 51.
Write down 3 as next digit of the result. 
Result so far: 54358.133
The remainder is 51 after subtracting 1059 from 1110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

In conclusion, the division gives 54358.133 with a balance of 0.0051.