We're dividing 787582 by 9 
Let's see how many times 9 fits into 787582.

Step 1:
If we divide 7 by 9, we get 0 and a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Grab the next digit (8) from the dividend, add it to 7, then carry on: 78 / 9

On to step 2:
9 goes into 78 8 times with a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
If we take 72 away from 78, we end up with 6.
Include the next digit (7) from the dividend after 6, then repeat: 67 / 9

Going ahead to step 3:
When dividing 67 by 9, we get 7 with a remainder of 4.
The next digit of our result is 7. 
Result so far: 87.0
If we take 63 away from 67, we end up with 4.
Grab the next digit (5) from the dividend, add it to 4, then carry on: 45 / 9

Moving on to step 4:
When dividing 45 by 9, we get 5 with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 875.0
If we take 45 away from 45, we end up with 0.
Grab the next digit (8) from the dividend, add it to 0, then carry on: 8 / 9

Step 5:
9 can be fit into 8 0 times, resulting in a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 8750.0
If we take 0 away from 8, we end up with 8.
Grab the next digit (2) from the dividend, add it to 8, then carry on: 82 / 9

On to step 6:
If we divide 82 by 9, we get 9 and a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 87509.0
If we take 81 away from 82, we end up 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.

Step 7:
The number 9 fits into 10 1 times, leaving a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 87509.1
Subtract 9 from 10 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 8:
If we divide 10 by 9, we get 1 and a remainder of 1.
The next digit of our result is 1. 
Result so far: 87509.11
Subtract 9 from 10 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The quotient of the division is 87509.11, and the remainder is 0.001.