75644 divided by 13 
We're looking to find how many times 13 goes into 75644.

Going ahead to step 1:
If we divide 7 by 13, we get 0 and a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 13

Advancing to step 2:
When dividing 75 by 13, we get 5 with a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Subtracting 65 from 75 leaves us with 10.
Grab the next digit (6) from the dividend, add it to 10, then carry on: 106 / 13

Going ahead to step 3:
106 divided by 13 is 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 58.0
If we subtract 104 from 106, we get 2.
Append the next digit (4) from the dividend to 2 and continue with: 24 / 13

Step 4:
13 can be fit into 24 1 times, resulting in a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 581.0
Deduct 13 from 24 and we're left with 11.
Fetch the next digit (4) from the dividend, attach it to 11 and continue: 114 / 13

Let's proceed to step 5:
If we divide 114 by 13, we get 8 and a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 5818.0
If we subtract 104 from 114, we 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.

On to step 6:
13 goes into 100 7 times with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 5818.7
Subtract 91 from 100 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 7:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 5818.76
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.

Let's proceed to step 8:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 5818.769
Deduct 117 from 120 and we're left 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.

Let's proceed to step 9:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 5818.7692
Subtract 26 from 30 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 10:
40 divided by 13 is 3 with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 5818.76923
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.

On to step 11:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 5818.76923
If we subtract 0 from 10, we 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.

On to step 12:
100 divided by 13 is 7 with a remainder of 9.
The next digit of our result is 7. 
Result so far: 5818.7692307
Deduct 91 from 100 and we're left 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 13:
90 divided by 13 is 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 5818.76923076
If we subtract 78 from 90, we 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.

The quotient of the division is 5818.76923076, and the remainder is 1.2e-08.