We look at the division of 349903 by 61 
Let's see how many times 61 fits into 349903.

Let's proceed to step 1:
When dividing 3 by 61, we get 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 61

Going ahead to step 2:
61 can be fit into 34 0 times, resulting in a remainder of 34.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 34, we get 34.
Take the next digit (9) from the dividend and append it to 34, then repeat: 349 / 61

Moving on to step 3:
61 goes into 349 5 times with a remainder of 44.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtract 305 from 349 to get 44.
Bring next digit (9) of the dividend behind the 44 and repeat the process: 449 / 61

Moving on to step 4:
The number 61 fits into 449 7 times, leaving a remainder of 22.
Use 7 as the next digit of our solution. 
Result so far: 57.0
Subtracting 427 from 449 leaves us with 22.
Bring next digit (0) of the dividend behind the 22 and repeat the process: 220 / 61

Step 5:
220 divided by 61 is 3 with a remainder of 37.
Write down 3 as next digit of the result. 
Result so far: 573.0
Subtracting 183 from 220 leaves us with 37.
Fetch the next digit (3) from the dividend, attach it to 37 and continue: 373 / 61

Advancing to step 6:
373 divided by 61 is 6 with a remainder of 7.
Put 6 as the next digit of the answer. 
Result so far: 5736.0
Deduct 366 from 373 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 7:
70 divided by 61 is 1 with a remainder of 9.
The next digit of our result is 1. 
Result so far: 5736.1
Subtract 61 from 70 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 8:
If we divide 90 by 61, we get 1 and a remainder of 29.
Record the quotient 1 as the next digit in the result. 
Result so far: 5736.11
Subtract 61 from 90 to get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

After the division, we end up with 5736.11 and a remainder of 0.029.