598638 ÷ 65 
Our goal is to divide 598638 by 65.

On to step 1:
5 divided by 65 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (9) from the dividend to 5 and continue with: 59 / 65

Moving on to step 2:
65 goes into 59 0 times with a remainder of 59.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 59, we get 59.
Include the next digit (8) from the dividend after 59, then repeat: 598 / 65

Advancing to step 3:
If we divide 598 by 65, we get 9 and a remainder of 13.
Write down 9 as next digit of the result. 
Result so far: 9.0
The remainder is 13 after subtracting 585 from 598.
Grab the next digit (6) from the dividend, add it to 13, then carry on: 136 / 65

On to step 4:
65 can be fit into 136 2 times, resulting in a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 92.0
If we take 130 away from 136, we end up with 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 65

Going ahead to step 5:
The number 65 fits into 63 0 times, leaving a remainder of 63.
Put 0 as the next digit of the answer. 
Result so far: 920.0
Deduct 0 from 63 and we're left with 63.
Include the next digit (8) from the dividend after 63, then repeat: 638 / 65

Moving on to step 6:
65 goes into 638 9 times with a remainder of 53.
The next digit of our result is 9. 
Result so far: 9209.0
Subtracting 585 from 638 leaves us with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Going ahead to step 7:
When dividing 530 by 65, we get 8 with a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 9209.8
If we take 520 away from 530, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
The number 65 fits into 100 1 times, leaving a remainder of 35.
The next digit of our result is 1. 
Result so far: 9209.81
The remainder is 35 after subtracting 65 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 9:
65 goes into 350 5 times with a remainder of 25.
Put 5 as the next digit of the answer. 
Result so far: 9209.815
Subtract 325 from 350 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 10:
65 can be fit into 250 3 times, resulting in a remainder of 55.
The next digit of our result is 3. 
Result so far: 9209.8153
If we subtract 195 from 250, we get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 11:
65 goes into 550 8 times with a remainder of 30.
Record the quotient 8 as the next digit in the result. 
Result so far: 9209.81538
The remainder is 30 after subtracting 520 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 12:
300 divided by 65 is 4 with a remainder of 40.
The next digit of our result is 4. 
Result so far: 9209.815384
Deduct 260 from 300 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 13:
400 divided by 65 is 6 with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 9209.8153846
If we take 390 away from 400, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 14:
The number 65 fits into 100 1 times, leaving a remainder of 35.
Use 1 as the next digit of our solution. 
Result so far: 9209.81538461
Subtracting 65 from 100 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Our division results in 9209.81538461 with a remaining 3.5e-08.