We look at the division of 644731 by 519 
We're looking to find how many times 519 goes into 644731.

Going ahead to step 1:
The number 519 fits into 6 0 times, leaving a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 519

Step 2:
519 goes into 64 0 times with a remainder of 64.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 64 leaves us with 64.
Append the next digit (4) from the dividend to 64 and continue with: 644 / 519

Going ahead to step 3:
519 can be fit into 644 1 times, resulting in a remainder of 125.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 519 from 644 leaves us with 125.
Include the next digit (7) from the dividend after 125, then repeat: 1257 / 519

On to step 4:
The number 519 fits into 1257 2 times, leaving a remainder of 219.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Subtract 1038 from 1257 to get 219.
Grab the next digit (3) from the dividend, add it to 219, then carry on: 2193 / 519

Going ahead to step 5:
519 goes into 2193 4 times with a remainder of 117.
The next digit of our result is 4. 
Result so far: 124.0
Subtracting 2076 from 2193 leaves us with 117.
Include the next digit (1) from the dividend after 117, then repeat: 1171 / 519

Advancing to step 6:
When dividing 1171 by 519, we get 2 with a remainder of 133.
The next digit of our result is 2. 
Result so far: 1242.0
If we subtract 1038 from 1171, we get 133.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1330, and continue the process.

Advancing to step 7:
If we divide 1330 by 519, we get 2 and a remainder of 292.
Write down 2 as next digit of the result. 
Result so far: 1242.2
If we subtract 1038 from 1330, we get 292.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2920, and continue the process.

Advancing to step 8:
2920 divided by 519 is 5 with a remainder of 325.
Use 5 as the next digit of our solution. 
Result so far: 1242.25
If we take 2595 away from 2920, we end up with 325.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3250, and continue the process.

Let's proceed to step 9:
When dividing 3250 by 519, we get 6 with a remainder of 136.
The number 6 becomes the next digit in our result. 
Result so far: 1242.256
If we take 3114 away from 3250, we end up with 136.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1360, and continue the process.

Step 10:
519 can be fit into 1360 2 times, resulting in a remainder of 322.
Put 2 as the next digit of the answer. 
Result so far: 1242.2562
Subtract 1038 from 1360 to get 322.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3220, and continue the process.

Moving on to step 11:
If we divide 3220 by 519, we get 6 and a remainder of 106.
Put 6 as the next digit of the answer. 
Result so far: 1242.25626
If we subtract 3114 from 3220, we get 106.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1060, and continue the process.

Step 12:
519 goes into 1060 2 times with a remainder of 22.
Record the quotient 2 as the next digit in the result. 
Result so far: 1242.256262
Subtract 1038 from 1060 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 13:
220 divided by 519 is 0 with a remainder of 220.
Record the quotient 0 as the next digit in the result. 
Result so far: 1242.256262
If we subtract 0 from 220, we get 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2200, and continue the process.

Advancing to step 14:
2200 divided by 519 is 4 with a remainder of 124.
The number 4 becomes the next digit in our result. 
Result so far: 1242.25626204
The remainder is 124 after subtracting 2076 from 2200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1240, and continue the process.

In conclusion, the division gives 1242.25626204 with a balance of 1.24e-07.