We look at the division of 76781 by 15 
Let's see how many times 15 fits into 76781.

Going ahead to step 1:
When dividing 7 by 15, we get 0 with a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Append the next digit (6) from the dividend to 7 and continue with: 76 / 15

Advancing to step 2:
15 goes into 76 5 times with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtracting 75 from 76 leaves us with 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 15

On to step 3:
17 divided by 15 is 1 with a remainder of 2.
The next digit of our result is 1. 
Result so far: 51.0
If we subtract 15 from 17, we get 2.
Append the next digit (8) from the dividend to 2 and continue with: 28 / 15

Step 4:
The number 15 fits into 28 1 times, leaving a remainder of 13.
The next digit of our result is 1. 
Result so far: 511.0
Subtracting 15 from 28 leaves us with 13.
Fetch the next digit (1) from the dividend, attach it to 13 and continue: 131 / 15

On to step 5:
The number 15 fits into 131 8 times, leaving a remainder of 11.
The number 8 becomes the next digit in our result. 
Result so far: 5118.0
Subtracting 120 from 131 leaves us 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 6:
15 can be fit into 110 7 times, resulting in a remainder of 5.
Put 7 as the next digit of the answer. 
Result so far: 5118.7
If we take 105 away from 110, we end up with 5.
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 7:
When dividing 50 by 15, we get 3 with a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 5118.73
Subtracting 45 from 50 leaves us with 5.
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 8:
15 can be fit into 50 3 times, resulting in a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 5118.733
Deduct 45 from 50 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Our division results in 5118.733 with a remaining 0.0005.