We're dividing 15777 by 13 
Our goal is to divide 15777 by 13.

Going ahead to step 1:
13 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (5) from the dividend and append it to 1, then repeat: 15 / 13

On to step 2:
15 divided by 13 is 1 with a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 13 from 15 leaves us with 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 13

Going ahead to step 3:
13 can be fit into 27 2 times, resulting in a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 12.0
The remainder is 1 after subtracting 26 from 27.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 13

Moving on to step 4:
The number 13 fits into 17 1 times, leaving a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 121.0
Subtract 13 from 17 to get 4.
Grab the next digit (7) from the dividend, add it to 4, then carry on: 47 / 13

On to step 5:
If we divide 47 by 13, we get 3 and a remainder of 8.
Write down 3 as next digit of the result. 
Result so far: 1213.0
Subtract 39 from 47 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.

On to step 6:
If we divide 80 by 13, we get 6 and a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 1213.6
Deduct 78 from 80 and we're left 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.

On to step 7:
20 divided by 13 is 1 with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 1213.61
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.

On to step 8:
When dividing 70 by 13, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 1213.615
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.

On to step 9:
If we divide 50 by 13, we get 3 and a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 1213.6153
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 10:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 1213.61538
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.

Going ahead to step 11:
13 goes into 60 4 times with a remainder of 8.
The next digit of our result is 4. 
Result so far: 1213.615384
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.

Let's proceed to step 12:
The number 13 fits into 80 6 times, leaving a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 1213.6153846
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 13:
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: 1213.61538461
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.

The final result is 1213.61538461 with a remainder of 7e-09.