106971 divided by 87 
Our goal is to divide 106971 by 87.

Advancing to step 1:
The number 87 fits into 1 0 times, leaving a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 87

Moving on to step 2:
87 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Take the next digit (6) from the dividend and append it to 10, then repeat: 106 / 87

Going ahead to step 3:
When dividing 106 by 87, we get 1 with a remainder of 19.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 87 away from 106, we end up with 19.
Append the next digit (9) from the dividend to 19 and continue with: 199 / 87

Advancing to step 4:
If we divide 199 by 87, we get 2 and a remainder of 25.
Write down 2 as next digit of the result. 
Result so far: 12.0
Deduct 174 from 199 and we're left with 25.
Bring next digit (7) of the dividend behind the 25 and repeat the process: 257 / 87

Step 5:
If we divide 257 by 87, we get 2 and a remainder of 83.
The number 2 becomes the next digit in our result. 
Result so far: 122.0
If we take 174 away from 257, we end up with 83.
Fetch the next digit (1) from the dividend, attach it to 83 and continue: 831 / 87

Step 6:
When dividing 831 by 87, we get 9 with a remainder of 48.
Record the quotient 9 as the next digit in the result. 
Result so far: 1229.0
Deduct 783 from 831 and we're left with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Moving on to step 7:
87 can be fit into 480 5 times, resulting in a remainder of 45.
Write down 5 as next digit of the result. 
Result so far: 1229.5
If we take 435 away from 480, we end up with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Going ahead to step 8:
87 goes into 450 5 times with a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 1229.55
The remainder is 15 after subtracting 435 from 450.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

The quotient of the division is 1229.55, and the remainder is 0.015.