353819 ÷ 61 
We want to divide 353819 by 61.

Step 1:
The number 61 fits into 3 0 times, leaving a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 61

Step 2:
61 can be fit into 35 0 times, resulting in a remainder of 35.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 35, we get 35.
Fetch the next digit (3) from the dividend, attach it to 35 and continue: 353 / 61

Step 3:
The number 61 fits into 353 5 times, leaving a remainder of 48.
Put 5 as the next digit of the answer. 
Result so far: 5.0
If we subtract 305 from 353, we get 48.
Fetch the next digit (8) from the dividend, attach it to 48 and continue: 488 / 61

Let's proceed to step 4:
61 goes into 488 8 times with a remainder of 0.
Put 8 as the next digit of the answer. 
Result so far: 58.0
If we take 488 away from 488, we end up with 0.
Include the next digit (1) from the dividend after 0, then repeat: 1 / 61

Step 5:
When dividing 1 by 61, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 580.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (9) from the dividend, attach it to 1 and continue: 19 / 61

Advancing to step 6:
When dividing 19 by 61, we get 0 with a remainder of 19.
Record the quotient 0 as the next digit in the result. 
Result so far: 5800.0
If we subtract 0 from 19, we get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

On to step 7:
61 goes into 190 3 times with a remainder of 7.
Write down 3 as next digit of the result. 
Result so far: 5800.3
Subtract 183 from 190 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 8:
If we divide 70 by 61, we get 1 and a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 5800.31
The remainder is 9 after subtracting 61 from 70.
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 9:
The number 61 fits into 90 1 times, leaving a remainder of 29.
Record the quotient 1 as the next digit in the result. 
Result so far: 5800.311
The remainder is 29 after subtracting 61 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

The quotient of the division is 5800.311, and the remainder is 0.0029.