We're dividing 461340 by 13 
We want to figure out the number of times 461340 can be divided by 13.

Moving on to step 1:
13 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Append the next digit (6) from the dividend to 4 and continue with: 46 / 13

Step 2:
When dividing 46 by 13, we get 3 with a remainder of 7.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 7 after subtracting 39 from 46.
Grab the next digit (1) from the dividend, add it to 7, then carry on: 71 / 13

Step 3:
The number 13 fits into 71 5 times, leaving a remainder of 6.
Put 5 as the next digit of the answer. 
Result so far: 35.0
Subtracting 65 from 71 leaves us with 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 13

Step 4:
The number 13 fits into 63 4 times, leaving a remainder of 11.
Use 4 as the next digit of our solution. 
Result so far: 354.0
Subtract 52 from 63 to get 11.
Include the next digit (4) from the dividend after 11, then repeat: 114 / 13

Moving on to step 5:
If we divide 114 by 13, we get 8 and a remainder of 10.
Use 8 as the next digit of our solution. 
Result so far: 3548.0
If we subtract 104 from 114, we get 10.
Grab the next digit (0) from the dividend, add it to 10, then carry on: 100 / 13

Going ahead to step 6:
100 divided by 13 is 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 35487.0
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 7:
13 goes into 90 6 times with a remainder of 12.
The next digit of our result is 6. 
Result so far: 35487.6
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 8:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 35487.69
If we take 117 away from 120, we end up 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.

Moving on to step 9:
30 divided by 13 is 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 35487.692
Subtracting 26 from 30 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 10:
40 divided by 13 is 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 35487.6923
If we subtract 39 from 40, 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.

Let's proceed to step 11:
If we divide 10 by 13, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 35487.6923
Subtract 0 from 10 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.

Let's proceed to step 12:
13 goes into 100 7 times with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 35487.692307
If we take 91 away from 100, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 13:
When dividing 90 by 13, we get 6 with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 35487.6923076
Subtracting 78 from 90 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 14:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 35487.69230769
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Our division results in 35487.69230769 with a remaining 3e-09.