We divide 461689 by 15
We want to figure out the number of times 461689 can be divided by 15.

Advancing to step 1:
4 divided by 15 is 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Append the next digit (6) from the dividend to 4 and continue with: 46 / 15

Let's proceed to step 2:
46 divided by 15 is 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Subtracting 45 from 46 leaves us with 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 15

On to step 3:
When dividing 11 by 15, we get 0 with a remainder of 11.
The number 0 becomes the next digit in our result. 
Result so far: 30.0
If we subtract 0 from 11, we get 11.
Fetch the next digit (6) from the dividend, attach it to 11 and continue: 116 / 15

Step 4:
The number 15 fits into 116 7 times, leaving a remainder of 11.
Use 7 as the next digit of our solution. 
Result so far: 307.0
Deduct 105 from 116 and we're left with 11.
Fetch the next digit (8) from the dividend, attach it to 11 and continue: 118 / 15

Step 5:
If we divide 118 by 15, we get 7 and a remainder of 13.
Record the quotient 7 as the next digit in the result. 
Result so far: 3077.0
Subtracting 105 from 118 leaves us with 13.
Fetch the next digit (9) from the dividend, attach it to 13 and continue: 139 / 15

Let's proceed to step 6:
15 goes into 139 9 times with a remainder of 4.
The number 9 becomes the next digit in our result. 
Result so far: 30779.0
If we subtract 135 from 139, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
15 goes into 40 2 times with a remainder of 10.
Record the quotient 2 as the next digit in the result. 
Result so far: 30779.2
Subtract 30 from 40 to 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.

Moving on to step 8:
15 can be fit into 100 6 times, resulting in a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 30779.26
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.

Step 9:
If we divide 100 by 15, we get 6 and a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 30779.266
Deduct 90 from 100 and we're left 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 30779.266, and the remainder is 0.001.