6598 ÷ 45 
We want to divide 6598 by 45.

Going ahead to step 1:
45 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 45

Step 2:
If we divide 65 by 45, we get 1 and a remainder of 20.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 45 away from 65, we end up with 20.
Append the next digit (9) from the dividend to 20 and continue with: 209 / 45

Moving on to step 3:
When dividing 209 by 45, we get 4 with a remainder of 29.
Use 4 as the next digit of our solution. 
Result so far: 14.0
If we subtract 180 from 209, we get 29.
Grab the next digit (8) from the dividend, add it to 29, then carry on: 298 / 45

Moving on to step 4:
The number 45 fits into 298 6 times, leaving a remainder of 28.
The next digit of our result is 6. 
Result so far: 146.0
If we take 270 away from 298, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 5:
When dividing 280 by 45, we get 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 146.6
If we subtract 270 from 280, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 6:
45 can be fit into 100 2 times, resulting in a remainder of 10.
Record the quotient 2 as the next digit in the result. 
Result so far: 146.62
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 7:
45 can be fit into 100 2 times, resulting in a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 146.622
Subtracting 90 from 100 leaves us 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.

The quotient of the division is 146.622, and the remainder is 0.001.