We're dividing 87413 by 13 
We want to divide 87413 by 13.

On to step 1:
13 goes into 8 0 times with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Take the next digit (7) from the dividend and append it to 8, then repeat: 87 / 13

Advancing to step 2:
The number 13 fits into 87 6 times, leaving a remainder of 9.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we take 78 away from 87, we end up with 9.
Fetch the next digit (4) from the dividend, attach it to 9 and continue: 94 / 13

Moving on to step 3:
If we divide 94 by 13, we get 7 and a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 67.0
The remainder is 3 after subtracting 91 from 94.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 13

Going ahead to step 4:
13 can be fit into 31 2 times, resulting in a remainder of 5.
The next digit of our result is 2. 
Result so far: 672.0
Deduct 26 from 31 and we're left with 5.
Append the next digit (3) from the dividend to 5 and continue with: 53 / 13

Moving on to step 5:
When dividing 53 by 13, we get 4 with a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 6724.0
Deduct 52 from 53 and we're left with 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 6:
When dividing 10 by 13, we get 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 6724.0
If we take 0 away from 10, we end up 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 7:
When dividing 100 by 13, we get 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 6724.07
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.

On to step 8:
When dividing 90 by 13, we get 6 with a remainder of 12.
The next digit of our result is 6. 
Result so far: 6724.076
The remainder is 12 after subtracting 78 from 90.
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 9:
120 divided by 13 is 9 with a remainder of 3.
The next digit of our result is 9. 
Result so far: 6724.0769
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.

On to step 10:
30 divided by 13 is 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 6724.07692
If we take 26 away from 30, we end up 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.

Advancing to step 11:
13 goes into 40 3 times with a remainder of 1.
The next digit of our result is 3. 
Result so far: 6724.076923
The remainder is 1 after subtracting 39 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 12:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 6724.076923
If we take 0 away from 10, we end up 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.

On to step 13:
If we divide 100 by 13, we get 7 and a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 6724.07692307
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.

The final result is 6724.07692307 with a remainder of 9e-09.