4639603 ÷ 705 
Let's see how many times 705 fits into 4639603.

Moving on to step 1:
The number 705 fits into 4 0 times, leaving a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Grab the next digit (6) from the dividend, add it to 4, then carry on: 46 / 705

On to step 2:
The number 705 fits into 46 0 times, leaving a remainder of 46.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 46 and we're left with 46.
Grab the next digit (3) from the dividend, add it to 46, then carry on: 463 / 705

Advancing to step 3:
When dividing 463 by 705, we get 0 with a remainder of 463.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 463, we end up with 463.
Grab the next digit (9) from the dividend, add it to 463, then carry on: 4639 / 705

On to step 4:
If we divide 4639 by 705, we get 6 and a remainder of 409.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 4230 from 4639 and we're left with 409.
Append the next digit (6) from the dividend to 409 and continue with: 4096 / 705

Going ahead to step 5:
If we divide 4096 by 705, we get 5 and a remainder of 571.
Use 5 as the next digit of our solution. 
Result so far: 65.0
If we take 3525 away from 4096, we end up with 571.
Take the next digit (0) from the dividend and append it to 571, then repeat: 5710 / 705

Advancing to step 6:
5710 divided by 705 is 8 with a remainder of 70.
Record the quotient 8 as the next digit in the result. 
Result so far: 658.0
Subtract 5640 from 5710 to get 70.
Fetch the next digit (3) from the dividend, attach it to 70 and continue: 703 / 705

Going ahead to step 7:
705 can be fit into 703 0 times, resulting in a remainder of 703.
The next digit of our result is 0. 
Result so far: 6580.0
Subtract 0 from 703 to get 703.
Since there are no more digits in the dividend, we add a zero to the remainder making it 7030, and continue the process.

Advancing to step 8:
If we divide 7030 by 705, we get 9 and a remainder of 685.
Use 9 as the next digit of our solution. 
Result so far: 6580.9
Deduct 6345 from 7030 and we're left with 685.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6850, and continue the process.

Let's proceed to step 9:
705 goes into 6850 9 times with a remainder of 505.
The number 9 becomes the next digit in our result. 
Result so far: 6580.99
Deduct 6345 from 6850 and we're left with 505.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5050, and continue the process.

The quotient of the division is 6580.99, and the remainder is 0.505.