We look at the division of 460261 by 15 
We want to figure out the number of times 460261 can be divided by 15.

Advancing to step 1:
4 divided by 15 is 0 with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Fetch the next digit (6) from the dividend, attach it to 4 and continue: 46 / 15

Step 2:
If we divide 46 by 15, we get 3 and a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 3.0
Deduct 45 from 46 and we're left with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 15

Moving on to step 3:
10 divided by 15 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 30.0
Deduct 0 from 10 and we're left with 10.
Take the next digit (2) from the dividend and append it to 10, then repeat: 102 / 15

Step 4:
15 goes into 102 6 times with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 306.0
Subtract 90 from 102 to get 12.
Bring next digit (6) of the dividend behind the 12 and repeat the process: 126 / 15

Step 5:
15 can be fit into 126 8 times, resulting in a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 3068.0
Deduct 120 from 126 and we're left with 6.
Include the next digit (1) from the dividend after 6, then repeat: 61 / 15

Advancing to step 6:
61 divided by 15 is 4 with a remainder of 1.
The next digit of our result is 4. 
Result so far: 30684.0
If we subtract 60 from 61, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
If we divide 10 by 15, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 30684.0
Subtracting 0 from 10 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 8:
The number 15 fits into 100 6 times, leaving a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 30684.06
Subtract 90 from 100 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.

Step 9:
15 can be fit into 100 6 times, resulting in a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 30684.066
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 final result is 30684.066 with a remainder of 0.001.