87609591 ÷ 771 
Our goal is to divide 87609591 by 771.

Let's proceed to step 1:
771 can be fit into 8 0 times, resulting in a remainder of 8.
Record the quotient 0 as the next digit in the result. 
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 / 771

Advancing to step 2:
87 divided by 771 is 0 with a remainder of 87.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 87, we end up with 87.
Grab the next digit (6) from the dividend, add it to 87, then carry on: 876 / 771

Step 3:
876 divided by 771 is 1 with a remainder of 105.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 771 from 876 to get 105.
Fetch the next digit (0) from the dividend, attach it to 105 and continue: 1050 / 771

Step 4:
If we divide 1050 by 771, we get 1 and a remainder of 279.
Record the quotient 1 as the next digit in the result. 
Result so far: 11.0
If we subtract 771 from 1050, we get 279.
Fetch the next digit (9) from the dividend, attach it to 279 and continue: 2799 / 771

Let's proceed to step 5:
2799 divided by 771 is 3 with a remainder of 486.
The number 3 becomes the next digit in our result. 
Result so far: 113.0
If we subtract 2313 from 2799, we get 486.
Include the next digit (5) from the dividend after 486, then repeat: 4865 / 771

Step 6:
When dividing 4865 by 771, we get 6 with a remainder of 239.
The next digit of our result is 6. 
Result so far: 1136.0
Subtracting 4626 from 4865 leaves us with 239.
Grab the next digit (9) from the dividend, add it to 239, then carry on: 2399 / 771

Moving on to step 7:
If we divide 2399 by 771, we get 3 and a remainder of 86.
Write down 3 as next digit of the result. 
Result so far: 11363.0
Deduct 2313 from 2399 and we're left with 86.
Include the next digit (1) from the dividend after 86, then repeat: 861 / 771

Step 8:
771 goes into 861 1 times with a remainder of 90.
The number 1 becomes the next digit in our result. 
Result so far: 113631.0
If we subtract 771 from 861, we get 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

Let's proceed to step 9:
If we divide 900 by 771, we get 1 and a remainder of 129.
The number 1 becomes the next digit in our result. 
Result so far: 113631.1
Subtract 771 from 900 to get 129.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1290, and continue the process.

Advancing to step 10:
771 goes into 1290 1 times with a remainder of 519.
Record the quotient 1 as the next digit in the result. 
Result so far: 113631.11
If we take 771 away from 1290, we end up with 519.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5190, and continue the process.

Our division results in 113631.11 with a remaining 0.519.