We're dividing 460975 by 13 
We want to divide 460975 by 13.

Advancing to step 1:
13 goes into 4 0 times with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 13

Let's proceed to step 2:
If we divide 46 by 13, we get 3 and a remainder of 7.
The next digit of our result is 3. 
Result so far: 3.0
Subtract 39 from 46 to get 7.
Take the next digit (0) from the dividend and append it to 7, then repeat: 70 / 13

On to step 3:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 35.0
If we take 65 away from 70, we end up with 5.
Include the next digit (9) from the dividend after 5, then repeat: 59 / 13

On to step 4:
59 divided by 13 is 4 with a remainder of 7.
Use 4 as the next digit of our solution. 
Result so far: 354.0
Subtract 52 from 59 to get 7.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 13

Going ahead to step 5:
13 goes into 77 5 times with a remainder of 12.
The next digit of our result is 5. 
Result so far: 3545.0
The remainder is 12 after subtracting 65 from 77.
Include the next digit (5) from the dividend after 12, then repeat: 125 / 13

Advancing to step 6:
125 divided by 13 is 9 with a remainder of 8.
The number 9 becomes the next digit in our result. 
Result so far: 35459.0
Subtract 117 from 125 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 7:
If we divide 80 by 13, we get 6 and a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 35459.6
If we subtract 78 from 80, we 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.

Let's proceed to step 8:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 35459.61
If we take 13 away from 20, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 9:
13 goes into 70 5 times with a remainder of 5.
The next digit of our result is 5. 
Result so far: 35459.615
If we subtract 65 from 70, we get 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 10:
The number 13 fits into 50 3 times, leaving a remainder of 11.
The next digit of our result is 3. 
Result so far: 35459.6153
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 11:
13 goes into 110 8 times with a remainder of 6.
The next digit of our result is 8. 
Result so far: 35459.61538
Subtracting 104 from 110 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 12:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 35459.615384
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 13:
80 divided by 13 is 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 35459.6153846
Subtracting 78 from 80 leaves us with 2.
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 14:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 35459.61538461
Subtracting 13 from 20 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

In conclusion, the division gives 35459.61538461 with a balance of 7e-09.