We're dividing 458664 by 13 
We want to figure out the number of times 458664 can be divided by 13.

Let's proceed to step 1:
When dividing 4 by 13, we get 0 with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Grab the next digit (5) from the dividend, add it to 4, then carry on: 45 / 13

On to step 2:
The number 13 fits into 45 3 times, leaving a remainder of 6.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we subtract 39 from 45, we get 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 13

Advancing to step 3:
When dividing 68 by 13, we get 5 with a remainder of 3.
The number 5 becomes the next digit in our result. 
Result so far: 35.0
If we subtract 65 from 68, we get 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 13

Let's proceed to step 4:
13 goes into 36 2 times with a remainder of 10.
The next digit of our result is 2. 
Result so far: 352.0
If we subtract 26 from 36, we get 10.
Grab the next digit (6) from the dividend, add it to 10, then carry on: 106 / 13

Advancing to step 5:
The number 13 fits into 106 8 times, leaving a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 3528.0
If we subtract 104 from 106, we get 2.
Include the next digit (4) from the dividend after 2, then repeat: 24 / 13

Let's proceed to step 6:
When dividing 24 by 13, we get 1 with a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 35281.0
The remainder is 11 after subtracting 13 from 24.
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 7:
13 goes into 110 8 times with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 35281.8
Subtract 104 from 110 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 8:
13 goes into 60 4 times with a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 35281.84
If we take 52 away from 60, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 9:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 35281.846
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.

Advancing to step 10:
13 goes into 20 1 times with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 35281.8461
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 11:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 35281.84615
The remainder is 5 after subtracting 65 from 70.
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 12:
13 goes into 50 3 times with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 35281.846153
Deduct 39 from 50 and we're left with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 13:
110 divided by 13 is 8 with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 35281.8461538
Deduct 104 from 110 and we're left 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 14:
13 goes into 60 4 times with a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 35281.84615384
Subtract 52 from 60 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.

The quotient of the division is 35281.84615384, and the remainder is 8e-09.