We're dividing 351903 by 42 
We're looking to find how many times 42 goes into 351903.

Step 1:
42 can be fit into 3 0 times, resulting in a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 42

Let's proceed to step 2:
42 can be fit into 35 0 times, resulting in a remainder of 35.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 35, we get 35.
Take the next digit (1) from the dividend and append it to 35, then repeat: 351 / 42

On to step 3:
42 goes into 351 8 times with a remainder of 15.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Deduct 336 from 351 and we're left with 15.
Bring next digit (9) of the dividend behind the 15 and repeat the process: 159 / 42

Going ahead to step 4:
42 goes into 159 3 times with a remainder of 33.
The next digit of our result is 3. 
Result so far: 83.0
If we take 126 away from 159, we end up with 33.
Grab the next digit (0) from the dividend, add it to 33, then carry on: 330 / 42

Moving on to step 5:
330 divided by 42 is 7 with a remainder of 36.
The next digit of our result is 7. 
Result so far: 837.0
If we take 294 away from 330, we end up with 36.
Take the next digit (3) from the dividend and append it to 36, then repeat: 363 / 42

Advancing to step 6:
When dividing 363 by 42, we get 8 with a remainder of 27.
Put 8 as the next digit of the answer. 
Result so far: 8378.0
If we take 336 away from 363, we end up with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Advancing to step 7:
270 divided by 42 is 6 with a remainder of 18.
Put 6 as the next digit of the answer. 
Result so far: 8378.6
Subtracting 252 from 270 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 8:
If we divide 180 by 42, we get 4 and a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 8378.64
If we take 168 away from 180, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 9:
If we divide 120 by 42, we get 2 and a remainder of 36.
The number 2 becomes the next digit in our result. 
Result so far: 8378.642
If we subtract 84 from 120, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 10:
42 goes into 360 8 times with a remainder of 24.
Record the quotient 8 as the next digit in the result. 
Result so far: 8378.6428
The remainder is 24 after subtracting 336 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 11:
42 goes into 240 5 times with a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 8378.64285
If we take 210 away from 240, 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.

On to step 12:
42 goes into 300 7 times with a remainder of 6.
The number 7 becomes the next digit in our result. 
Result so far: 8378.642857
If we subtract 294 from 300, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 13:
If we divide 60 by 42, we get 1 and a remainder of 18.
Record the quotient 1 as the next digit in the result. 
Result so far: 8378.6428571
Subtract 42 from 60 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 14:
42 goes into 180 4 times with a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 8378.64285714
If we take 168 away from 180, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final outcome is 8378.64285714, with a leftover of 1.2e-08.