We look at the division of 63609 by 6 
We're looking to find how many times 6 goes into 63609.

Step 1:
If we divide 6 by 6, we get 1 and a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 6 from 6 leaves us with 0.
Grab the next digit (3) from the dividend, add it to 0, then carry on: 3 / 6

On to step 2:
The number 6 fits into 3 0 times, leaving a remainder of 3.
The next digit of our result is 0. 
Result so far: 10.0
If we take 0 away from 3, we end up with 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 6

Let's proceed to step 3:
6 can be fit into 36 6 times, resulting in a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 106.0
Deduct 36 from 36 and we're left with 0.
Grab the next digit (0) from the dividend, add it to 0, then carry on: 0 / 6

Step 4:
The number 6 fits into 0 0 times, leaving a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 1060.0
The remainder is 0 after subtracting 0 from 0.
Append the next digit (9) from the dividend to 0 and continue with: 9 / 6

Step 5:
6 goes into 9 1 times with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 10601.0
Deduct 6 from 9 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 6:
The number 6 fits into 30 5 times, leaving a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 10601.5
The remainder is 0 after subtracting 30 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 7:
When dividing 0 by 6, we get 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 10601.5
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 8:
6 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 10601.5
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 10601.5, and the remainder is 0.0.