581303 ÷ 738 
We're looking to find how many times 738 goes into 581303.

Advancing to step 1:
If we divide 5 by 738, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 738

Going ahead to step 2:
58 divided by 738 is 0 with a remainder of 58.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 58 and we're left with 58.
Bring next digit (1) of the dividend behind the 58 and repeat the process: 581 / 738

On to step 3:
738 can be fit into 581 0 times, resulting in a remainder of 581.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 581 and we're left with 581.
Append the next digit (3) from the dividend to 581 and continue with: 5813 / 738

Let's proceed to step 4:
5813 divided by 738 is 7 with a remainder of 647.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Subtract 5166 from 5813 to get 647.
Include the next digit (0) from the dividend after 647, then repeat: 6470 / 738

Moving on to step 5:
The number 738 fits into 6470 8 times, leaving a remainder of 566.
The number 8 becomes the next digit in our result. 
Result so far: 78.0
The remainder is 566 after subtracting 5904 from 6470.
Grab the next digit (3) from the dividend, add it to 566, then carry on: 5663 / 738

On to step 6:
5663 divided by 738 is 7 with a remainder of 497.
Use 7 as the next digit of our solution. 
Result so far: 787.0
If we subtract 5166 from 5663, we get 497.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4970, and continue the process.

On to step 7:
738 can be fit into 4970 6 times, resulting in a remainder of 542.
Write down 6 as next digit of the result. 
Result so far: 787.6
Deduct 4428 from 4970 and we're left with 542.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5420, and continue the process.

Moving on to step 8:
738 can be fit into 5420 7 times, resulting in a remainder of 254.
Use 7 as the next digit of our solution. 
Result so far: 787.67
Deduct 5166 from 5420 and we're left with 254.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2540, and continue the process.

Going ahead to step 9:
2540 divided by 738 is 3 with a remainder of 326.
Record the quotient 3 as the next digit in the result. 
Result so far: 787.673
If we subtract 2214 from 2540, we get 326.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3260, and continue the process.

On to step 10:
The number 738 fits into 3260 4 times, leaving a remainder of 308.
Put 4 as the next digit of the answer. 
Result so far: 787.6734
Deduct 2952 from 3260 and we're left with 308.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3080, and continue the process.

Going ahead to step 11:
738 goes into 3080 4 times with a remainder of 128.
Write down 4 as next digit of the result. 
Result so far: 787.67344
Deduct 2952 from 3080 and we're left with 128.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1280, and continue the process.

The final result is 787.67344 with a remainder of 0.000128.