We look at the division of 705759 by 45 
Our goal is to divide 705759 by 45.

Going ahead to step 1:
The number 45 fits into 7 0 times, leaving a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Include the next digit (0) from the dividend after 7, then repeat: 70 / 45

Step 2:
45 can be fit into 70 1 times, resulting in a remainder of 25.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 25 after subtracting 45 from 70.
Include the next digit (5) from the dividend after 25, then repeat: 255 / 45

On to step 3:
If we divide 255 by 45, we get 5 and a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 15.0
The remainder is 30 after subtracting 225 from 255.
Fetch the next digit (7) from the dividend, attach it to 30 and continue: 307 / 45

On to step 4:
If we divide 307 by 45, we get 6 and a remainder of 37.
Write down 6 as next digit of the result. 
Result so far: 156.0
Subtracting 270 from 307 leaves us with 37.
Include the next digit (5) from the dividend after 37, then repeat: 375 / 45

On to step 5:
375 divided by 45 is 8 with a remainder of 15.
Write down 8 as next digit of the result. 
Result so far: 1568.0
Subtracting 360 from 375 leaves us with 15.
Take the next digit (9) from the dividend and append it to 15, then repeat: 159 / 45

Advancing to step 6:
45 can be fit into 159 3 times, resulting in a remainder of 24.
The number 3 becomes the next digit in our result. 
Result so far: 15683.0
If we subtract 135 from 159, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 7:
The number 45 fits into 240 5 times, leaving a remainder of 15.
The next digit of our result is 5. 
Result so far: 15683.5
If we take 225 away from 240, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 8:
150 divided by 45 is 3 with a remainder of 15.
Use 3 as the next digit of our solution. 
Result so far: 15683.53
If we take 135 away from 150, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 9:
The number 45 fits into 150 3 times, leaving a remainder of 15.
Record the quotient 3 as the next digit in the result. 
Result so far: 15683.533
The remainder is 15 after subtracting 135 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

The final result is 15683.533 with a remainder of 0.0015.