705597 ÷ 45 
We're looking to find how many times 45 goes into 705597.

On to step 1:
45 goes into 7 0 times with a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Bring next digit (0) of the dividend behind the 7 and repeat the process: 70 / 45

Going ahead to step 2:
The number 45 fits into 70 1 times, leaving a remainder of 25.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 45 from 70 to get 25.
Bring next digit (5) of the dividend behind the 25 and repeat the process: 255 / 45

On to step 3:
45 can be fit into 255 5 times, resulting in a remainder of 30.
The next digit of our result is 5. 
Result so far: 15.0
The remainder is 30 after subtracting 225 from 255.
Take the next digit (5) from the dividend and append it to 30, then repeat: 305 / 45

On to step 4:
45 goes into 305 6 times with a remainder of 35.
Use 6 as the next digit of our solution. 
Result so far: 156.0
If we take 270 away from 305, we end up with 35.
Grab the next digit (9) from the dividend, add it to 35, then carry on: 359 / 45

Advancing to step 5:
The number 45 fits into 359 7 times, leaving a remainder of 44.
Record the quotient 7 as the next digit in the result. 
Result so far: 1567.0
If we take 315 away from 359, we end up with 44.
Append the next digit (7) from the dividend to 44 and continue with: 447 / 45

Let's proceed to step 6:
447 divided by 45 is 9 with a remainder of 42.
Put 9 as the next digit of the answer. 
Result so far: 15679.0
Deduct 405 from 447 and we're left with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Going ahead to step 7:
420 divided by 45 is 9 with a remainder of 15.
The next digit of our result is 9. 
Result so far: 15679.9
Subtract 405 from 420 to get 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:
If we divide 150 by 45, we get 3 and a remainder of 15.
Record the quotient 3 as the next digit in the result. 
Result so far: 15679.93
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.

Going ahead to step 9:
45 can be fit into 150 3 times, resulting in a remainder of 15.
Record the quotient 3 as the next digit in the result. 
Result so far: 15679.933
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.

The final result is 15679.933 with a remainder of 0.0015.