Let's divide 10589 by 6
We want to figure out the number of times 10589 can be divided by 6.

Moving on to step 1:
The number 6 fits into 1 0 times, leaving a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 6

On to step 2:
When dividing 10 by 6, we get 1 with a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 6 from 10, we get 4.
Append the next digit (5) from the dividend to 4 and continue with: 45 / 6

Let's proceed to step 3:
45 divided by 6 is 7 with a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 17.0
The remainder is 3 after subtracting 42 from 45.
Take the next digit (8) from the dividend and append it to 3, then repeat: 38 / 6

Advancing to step 4:
6 can be fit into 38 6 times, resulting in a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 176.0
Subtracting 36 from 38 leaves us with 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 6

On to step 5:
29 divided by 6 is 4 with a remainder of 5.
The number 4 becomes the next digit in our result. 
Result so far: 1764.0
Subtracting 24 from 29 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 6:
50 divided by 6 is 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 1764.8
Subtract 48 from 50 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 7:
20 divided by 6 is 3 with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 1764.83
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
The number 6 fits into 20 3 times, leaving a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 1764.833
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The quotient of the division is 1764.833, and the remainder is 0.0002.