We divide 514097 by 759
We want to divide 514097 by 759.

Advancing to step 1:
The number 759 fits into 5 0 times, leaving a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 759

Moving on to step 2:
51 divided by 759 is 0 with a remainder of 51.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Append the next digit (4) from the dividend to 51 and continue with: 514 / 759

Step 3:
514 divided by 759 is 0 with a remainder of 514.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 514 and we're left with 514.
Grab the next digit (0) from the dividend, add it to 514, then carry on: 5140 / 759

Moving on to step 4:
5140 divided by 759 is 6 with a remainder of 586.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Deduct 4554 from 5140 and we're left with 586.
Fetch the next digit (9) from the dividend, attach it to 586 and continue: 5869 / 759

Step 5:
5869 divided by 759 is 7 with a remainder of 556.
The next digit of our result is 7. 
Result so far: 67.0
Subtract 5313 from 5869 to get 556.
Grab the next digit (7) from the dividend, add it to 556, then carry on: 5567 / 759

Going ahead to step 6:
When dividing 5567 by 759, we get 7 with a remainder of 254.
The next digit of our result is 7. 
Result so far: 677.0
Subtracting 5313 from 5567 leaves us 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.

Let's proceed to step 7:
If we divide 2540 by 759, we get 3 and a remainder of 263.
The next digit of our result is 3. 
Result so far: 677.3
Subtracting 2277 from 2540 leaves us with 263.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2630, and continue the process.

On to step 8:
When dividing 2630 by 759, we get 3 with a remainder of 353.
Record the quotient 3 as the next digit in the result. 
Result so far: 677.33
Subtracting 2277 from 2630 leaves us with 353.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3530, and continue the process.

After the division, we end up with 677.33 and a remainder of 0.353.